-------
o
I
NJ
20
Vehicle Weight = 4600 Ibs
0% Grade
18 Engine Accessories Include Air
Conditioner (Figure C-5)
Flywheel Losses per Figure C-3
16 Fuel Density = 6.152 Ib/gal
14
Pierced Flywheel, P = .581 psi
_ j:_
kF-
fi
10
. .;
.
i - :]__:-
4
2
0
;
-' ;""-i :, ! •'••":. . . ! "
trcrttttrrjtftti'' '•* ~
gfnjf
*T1 "^1 i
. I I
I'
i-;;::
•
'.
. - ~
10
20
j
J
30
,
L±tH _..:. i.
: --•-..::
• -—-r—
^p
rrrrt
tfJ.fnlr^i• '• • :."" '.'
fnTuiTT'" ' • "~~-;~
.-.-:
^^-"—- :. ;:-~fc 4"
' ,.
1
40 50
Vehicle Speed, MPH
60
-
., .
70
80
.
90.
Fig. C-12 Fuel Economy of Flywheel/Hybrid Propulsion System at Cruise Power
-------
Comparable steady-state cruise power performance calculations were made for a
conventional propulsion system with a conventional automatic transmission and
the same size 1C engine (defined by Figure C-4). It was assumed on a level
road at cruise power that the conventional automatic transmission was in first
gear at up to 10 MPH, second gear at 15 MPH and in third gear from 20 to 85 MPH.
Depending upon the particular characteristics of the transmission controls and
their design settings, Lt is quite possible that the automatic transmission
could be In third gear from 10 Lo 85 MPII til: c-.ruf.se conditions.
The resultant transmission efficiency calculated for the conventional automatic
transmission is shown by Figure C-13. The affect on transmission efficiency
of operating in various gears is clearly indicated. The corresponding fuel
economy is shown by Figure C-14.
A comparison between the transmission efficiency of the flywheel/hybrid and
conventional automatic transmissions is shown by Figure C-15. These results
indicate that the hybrid transmission design presented herein should be more
efficient than the automatic transmission particularly at cruiso speeds from
20 to 40 MPH. Although flywheel losses Lend to improve the ei'lMc i.ency of t lie
flywheel/hybrid transmission as noted earlier, the hydromechanics I (power-
splitting) transmission design used will sl.ill exhibit better efficiency at. low
vehicle speeds even without flywheel losses.
Figure C-16 presents a comparison of power train efficiencies at cruise power.
The affect of flywheel losses is clearly evident in the lower power train
efficiency of the flywheel/hybrid transmission at low vehicle speeds. These
results can be misleading since they do not indicate the relative effect upon
engine performance and emissions.
A more important comparison is on the basis of fuel economy. Figure C-17 pre-
sents this comparison at cruise power in terms of miles/gallon. The comparable
percentage change in fuel economy is then shown by Figure C-18 for two different
flywheel losses. These results indicate that, the flywheel/hybrid propulsion
system will have a decrease in cruise fuel economy at low vehicle speeds
C-22
-------
100
r>
to
Vehicle Weight = 4600 Ibs
07, Grade
Accessories Include Air Conditioner
(Figure C-5)
80
60
40
20
/
/
3rd Gear
— .„ . .
t
J
i
•
•
Solid Curve ( ) Indicates Standard
Automatic Transmission Efficiency Selected
for Cruise Power
i
• r ]
Dashed Curves ( ) Indicate Effect of
Staying in Various Gears
I
.
t . . \
(Transmission Output Power) x 100
Transmission Efficiency = - : f- —
Transmission Input Power
10
20
30
40 50
Vehicle Speed, MPH
60
70
80
90
Fig. C-13 Transmission Efficiency at Cruise Power — Conventional Automatic Transmission
-------
n
t-o
20
18
16
L4
|
o
§ 10
u
5J
Vehicle Weight = 4600 Ibs
0% Grade
Fuel Density = 6.152 Ib/gal.
Engine Accessories Include Air
Conditioner (Figure C-5)
Solid Curve Indicates Fuel Economy
With Standard Automatic Transmission
at Cruise Power
±jr.!
.. •},.
: _:
3 ^
"* 2nd Gear
;
Dashed Curves Indicate Effect
of Staying in Various Gears
!
.. ,i
:•
•
-__—i --^..*rr- -,: r 4-'*"—-"•"
.}—•:: -
i_lL^r:
jrr::,
,_ .^l-r-
• :—"I'. :
•
30
40 50
Vehicle Speed, MPH
60
.
70 80
_
"" - ; " . -
• •
' I
; •
90
Fig. C-14 Fuel Economy at Cruise Power — Conventional Automatic
Transmission (No Flywheel)
-------
100 ,
Flywheel/Hybrid Transmission
o
(With Inline Pierced Flywheel, P = 2.94 psi)
Standard Automatic Transmission (Without Flywheel)
1 • '
±±±t--hrri--r- -
: Vehicle Weight = 4600 Ibs
0% Grade
Engine Accessories Include Air Conditioner --
(HP + HP_, , ) x 100
out Fly-loss
Transmission Efficiency (Cruise)
40 50
Vehicle Speed, MPH
Fig. C-15 Comparison of Transmission Efficiencies at Cruise Power
MTI-12492
-------
100 ;
ro
CT
Standard Automatic Transmission
(Without Flywheel)
Flywheel/Hybrid Transmission Power Train
(With Inline Pierced Flywheel, P = 2.94 psi)
Cruise Power Train Efficiency =
I ,'- . T::/
10
20
30
40 50
Vehicle Speed, MPH
Fig. C-16 Power Train Efficiency Comparison at Cruise Power
MTI-12493
-------
o
20
18
16
14
12
10
f-.. ::••:
Vehicle Weight = 4600 Ibs
0% Grade
"Fuel Density = 6.152 Ib/gal
tut
"Engine Accessories Include Air Conditioner
^Standard Automatic Transmission
:r (Without Flywheel)
• • ' '
Flywheel/Hybrid Transmission
(With Inline Pierced Flywheel,£
40 50
Vehicle Speed, MPH
Fig. C-17 Comparison of Fuel Economy at Cruise Power
MTI-1249A
-------
20
n
ho
CO
•H
Steady-State Cruise Power
Vehicle Weight = 4600 Ibs
0% Grade
.Fuel Density = 6.152 Ib/gal.
Engine Accessories Include Air Conditioner
u
c
*
on
B
I
r«
I . _ t__
Pierced Flywheel. P
Pierced Flywheel, P = 2.94 psi
c
40 50
Vehicle Speed, MPH
Fig. C-18 Percentage Change in Cruise MPG Compared to Conventional
Automatic Power Train
MTI-12495
-------
(typically encountered in urban driving) compared to a conventional propulsion
system with an automatic transmission. The maximum decrease occurred at 20 MPH.
This loss in fuel economy is due to flywheel losses. For the higher loss fly-
wheel (Pc = 2.94 psi) the decrease in miles/gallon at 20 MPH was 18 percent.
Reducing the flywheel power losses by a total of 577» (see Figure C-3 earlier)
resulted in improved fuel economy, but it was still 10 percent less than the
conventional system at 20 MPH. Thus, even with the improved performance capa-
bilities of the variable ratio transmission (compared to the conventional auto-
matic), a decrease in cruise performance at low speeds can be expected. At
higher speeds, as shown by Figure C-18, an improvement up to nine percent in
fuel economy was obtained since flywheel losses are minimal.
A comparison of fuel flow used at idle by the existing heat engine/conventional
automatic transmission system and the heat engine/flywheel power-splitting
transmission system was made. The heat engine/flywheel system uses approximate-
ly 18 percent more fuel. The increased fuel flow is a direct result of the higher
idling speed for the flywheel system. The standard engine idles at 800 RPM,
has an idling torque requirement of approximately 85 foot-pounds and has a fuel
flow of 7.7 pounds per hour. The flywheel system idles at 1200 RPM, has a torque
requirement of 52 foot-pounds and a fuel flow of 9.2 pounds per hour.
The idling speed for the flywheel engine was selected to provide sufficient
engine horsepower to charge the flywheel within an acceptable time span. At
the speed selected, approximately 40 engine horsepower is available to charge
the flywheel. If the flywheel required a 20 percent makeup in energy this would
take approximately 12 seconds.
)
Any trade-off that would lower the hybrid system idling speed would reduce the
fuel flow and tend to equalize the idling performance of the two systems.
The flywheel/hybrid transmission was designed to allow the engine to operate at
minimum SFC whenever possible. Operation at minimum SFC was considered desirable
in order to minimize emissions. For the engine size specified by EPA/AAPS (see
Figure C-4) it was difficult to have engine operation at minimum SFC at low ••
C-29
-------
engine power requirements and: 1) transmit engine cruise power to the rear
wheels (and flywheel) at maximum efficiency; 2) have a minimum weight transmis-
sion; and 3) provide the capability of charging the flywheel at zero vehicle
speed.
A comparison of the engine SFC at cruise power is shown by Figure C-19. In
general, the flywheel/hybrid propulsion system tended to result in operation
closer to minimum SFC than the conventional system. At 10 MPH, a decrease of
20 to 32 percent in engine SFC was obtained dependent upon flywheel losses.
Operation at improved engine SFC was due to flywheel losses (more engine power
required) and the design features of the transmission.
The resultant engine horsepower required for the flywheel/hybrid propulsion
system at cruise conditions is given by Figure C-2Q. Also shown is the engine
horsepower required by a conventional system with a conventional automatic
transmission. Recall that flywheel losses and accessory losses were given
earlier, the maximum engine power at 3800 RPM is approximately 177 horsepower.
Thus, the 1C engine could have been reduced approximately 26 percent in size
for the flywheel/hybrid propulsion system and still meet the EPA/AAPS design
goals. Reducing flywheel losses will have little effect on the sizing of the
1C engine since at 70 MPH, the flywheel losses are relatively small.
It is important to point out that the reduced engine size required for the
f lywheeil/hybrid propulsion system could, perhaps, result in better cruise per-
formance than the results presented earlier. Further analysis is required in
order to determine whether such an improvement is possible.
3. Dynamic Performance
Before discussing the dynamic performance of the flywheel/hybrid propulsion
system, some fundamental differences between that system and a conventional
automotive propulsion system should be clarified. The basic concept of the
flywheel/hybrid system is that the flywheel supplies the kinetic energy to ac-
celerate the vehicle, and the heat engine only supplies that power required to
C-30
-------
50
40
Steady-State Cruise Power
Vehicle Weight = 4600 Ibs
0% Grade
Engine Accessories Include Air Conditioner
n
01
K
03
O
o 20
•Pierced Flywheel, P = 2.94 psi
10
Pierced Flywheel, P = 0.581 psi
40 50
Vehicle Speed, MPH
Fig. C-19 Percent Decrease in Cruise SFC Compared to
Conventional Automatic Power Train
KTI-12M9
-------
160
Engine Accessories Include Air Conditioner (Figure C-5)
Based on Inline Pierced Flywheel P =2.94 psi
140
a
8
w
•a
OJ
1-J
4600 Ib Vehicle
0% Grade
Standard Automatic Transmission
Without Flywheel
20
40 60
Vehicle Speed, MPH
100
120
Fig. C-20 Required Engine Power at Cruise Conditions
C-32
-------
provide steady-state power and to overcome system energy losses. These losses
include accessory, auxiliary, flywheel, transmission, air drag, and rolling
resistance losses. Since the torque (or power) developed by the flywheel is
proportional to its angularj acceleration, the flywheel produces no useful power
' dn
at steady-state conditions
dt
sion system, it is not feasible to
Unlike a conventional automotive propul-
obtain steady-state performance maps over the
complete output power spectrum of the flywheel/hybrid propulsion system. This
means that maximum torque output can only be achieved when flywheel and vehicle
speed are changing as a function of time.
Furthermore, the dynamic response of a flywheel/hybrid propulsion system for a
given engine, flywheel, and vehicle is primarily governed by the transmission
design characteristics and its associated controls. Design characteristics such
as the speed ratio are particularly important. With variable ratio transmissions,
the time rate of change of ratio can have a significant affect- ;ipon system rer
sponse during accelerations or decelerations.
Two types of vehicle operating modes can be considered in order to evaluate the
dynamic performance of the flywheel/hybrid propulsion system:
1. Maximum Performance defined by EPA/AAPS Design Goals (1).
2. Driving Cycle Performance defined by DHEW driving cycle.
Analytical determination of realistic performance characteristics for either
of these modes requires solution of torque and speed relationships in the time
domain. Comparison to a conventional propulsion system requires a similar
approach to be followed for the conventional system (&)•
Since the scope of this study was limited to determining transmission efficien-
cy, dynamic performance analysis was limited to the maximum power mode. This is
a "worst case" condition for.the transmission with respect to efficiency of
power transfer from the engine and flywheel. Also, it demonstrates the maximum
capabilities of the design.
C-33
-------
The dynamic results for the flywheel/hybrid propulsion system under
the maximum power mode were then cross-plotted versus vehicle speed so that
a comparison could be made to maximum power performance of a conventional
system with a standard automatic transmission.
As pointed out elsewhere in this report, the desired maximum power capability
of the transmission determines the size (capacity) of the hydraulic units in
the transmission. Hydraulic units were sized to meet the tractive effort re-
quirements given earlier by Figure C-l. Once a particular size is selected,
the maximum power throughout is limited by the pressure relief valve settings
in the hydraulic units. Thus, control characteristics in the secondary trans-
mission (governing the flywheel) must be selected so as to call for control
power outputs that do not exceed, except for very short durations, the maximum
capability of the hydraulic units in the secondary transmission. In addition,
the control characteristics must provide for stable operation of the complete
system with desired engine performance.
Pertinent characteristics of the full-range digital simulation of the propul-
sion system used to determine dynamic performance were as follows. The full-
power transient was initiated by a step input in the driver pedal commanding
*
a speed change from 8 to 85 MPH. Vehicle weight was 5300 pounds (per EPA/AAPS
Design Goals) operating on a level road. Engine accessory horsepower was given
earlier by Figure C-7. The flywheel was a pierced configuration operating at
2.
a chamber pressure of 2.94 psi with an inertia of 0.49 ft-lb-sec The 1C
engine used was defined earlier by Figure C-4. An engine inertia of
2
0.0568 ft-lb-sec , typical for that size engine, was assumed. Other inertias
*
A lower speed of 8 MPH was selected to safely avoid operation at lesser
speeds where the model was invalid.
C-34
-------
included in the dynamic model were the vehicle rear axle and differential,
vehicle wheels, and major rotating components in the transmission.
t4
The: control, system was the open loop scheduling or Type B (see Section Vl-D)
setup for TKE with the flywheel speed varying between 24,000 RPM ami 10,000 RPM
for vehicle speeds of 0 to 85 MPH, respectively. Control gains and rate limits
were adjusted in order to:
1. Provide a reasonable level of performance.
2. Avoid wheel slip (which was not simulated).
3. Stay within maximum power limitations of the transmission.
4. Provide engine power to make up for system losses.
5. Stay within control stability limits.
Additional tuning and optimization of the system controls would have easily
resulted in improved acceleration characteristics of the vehicle.
Fi r.urc- C-21 presents the resulting vehicle and flywheel speed transients Cor
36 seconds after the step change in driver pedal. The vehicle reached 60 MPH
in 1.4 seconds and 80 MPH in 26 seconds. This was slightly below the EPA/AAPS
goal of 0 to 60 MPH in 13.5 seconds. As previously mentioned, further tuning
of the controls (closer to wheel slip) would have resulted in achieving the goal
without altering the propulsion system. Since the average power developed at
the wheels from 25 to 80 MPH was 120 HP and within the limits specified by
LMSC (see Figure C-l) for that speed range, these data were considered represen-
tative of a full power transient.
As shown in Figure C-21, flywheel speed reached its minimum value (10,000 RPM)
prior to vehicle speed reaching 85 MPH. This was caused by the control system
in order to minimize excessive "undershoot" in flywheel speed. Lowest flywheel
speed was 9891 RPM at. 32 seconds. Thus, the maximum "undershoot" in flywheel
speed was only 1.1 percent less than the final steady-state speed. This demon-
strates quite acceptable control performance.
C-35
-------
o
110
100
90
80
70
ac
O-.
60
50
30
28
26
24
22
£ 20
18
a
in
u
•H
j:
16
.c
30
20
10
0 L
14
12
10
Step Change in Driver Pedal at t = 0
Vehicle Weight = 5300 Ibs
070 Grade
Pierced Flywheel, P = 2.94 psi
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Time, Seconds
Fig. C-21 Engine and Flywheel Speed During Full-Power Transient
MTt-' 514
-------
Referring again to Figure C-21 it- -.m be seen that at 36 seconds (end of com-
puter run) vehicle speed is within '.I'.ree percent and gradually approaching its
steady-state value of 85 mph. Final steady-state conditions would have been
reached in approximately another 14 seconds. This type of damped response is
desirable since it shows that as the system transient settles out, there are
no undesirable oscillations in vehicle speed.
The change in energy developed by the flywheel (less losses) and engine during
the transient is presented by Figure C-22. Table C- 1 presents an energy balance
for the transient for a vehicle speed change from 8 to 80 mph. The latter spp^d
was selected since the flywheel contribution was minimal at higher speeds as
shown by Figure C-22. These results indicate that during the full power transient:
1. Total energy transferred to the rear wheels was 2845 horsepower-seconds or
74 percent of the input energy from the flywheel and engine (3852 horsepow°r-
seconds). If accessory power is subtracted, 84 percent of the input energy
is transferred to the rear wheels.
2. The transmission and rear axle (power train) losses were 12 percent (475
horsepower-seconds) of the input energy. This resulted in an effective
power train efficiency of 86 percent calculated as follows:
.,.•=•<-«: 2845 x 100
Power Train Eff = o + 475 =
Dividing by the rear axle efficiency (96 percent) results in a transmission
efficiency of 89.5 percent on an energy transfer basis. Thus, the trans-
mission under full power transient conditions transferred energy to the
vehicle wheels at a relatively high efficiency.
3. Although control settings were not optimized, the engine supplied only 13
percent less energy than it should have in order to follow ideal TKE control;
the change in vehicle kinetic energy was 90 percent of the change in fly-
wheel energy. This can be seen by noting in Table C-l that the engine
supplied 1576 horsepower-seconds or 41 percent of the input energy required.
For perfect TKE control, the engine must supply the total energy input minus
the vehicle change in kinetic energy or 3852-2047 = 1805 horsepower seconds.
Similarly, the flywheel change in kinetic energy was 2276 horsepower-seconds,
while the vehicle change in kinetic energy was only 2047 horsepower seconds.
C-37
-------
Lo
OO
*ouu
2400
2200
2000
1800
1600
•o
c
o
0
% 1400
01
a 1200
n
i-i
o
x 1000
800
600
400
200
0
ill • T '
Step Change in Driver Pedal at t = 0
Vehicle Weight = 5300 Ibs
' 07. Grade
Pierced Flywheel, P = 2.94 psi
_-=:
/
' -
/
'
/
'
/
"
/
Net Energy Out
of Flywheel — ^
X
X
X
X
x
' /
x
X
/
^
^
.^^•k"
w
•
/
-
/
/
- Engine
Energy
/
/
0246 8 10 12 14 16 18 20 22
Time, Seconds
24 26 28 30 32 34
36
Fig. C-22 Change in Energy Produced by Engine and Flywheel
During Full Power Transient
HTI-12501
-------
TABLE C-I
Energy Balance for Full-Power Transient From 8 to 80 mph
Description
Change in Vehicle Kinetic Energy
Change in Engine Kinetic Energy
Flywheel Losses
Road Resistance & Air Drag Losses
Accessory Losses
Transmission & Rear End
(power train) Losses
Change in Flywheel Kinetic Energy
Change in Engine Energy
HP-Sec
2047
7
76
798
449
475
3852
2276
1576
3852
Percent
53
ft* 0
2
21
12
12
1007o
59
41
100%
C-39
-------
These results indicate the system approximated TKE control fairly close.
Further adjustments in control should provide somewhat better performance.
4. The combined energy from the flywheel and engine was 3852 horsepower sec-
onds (800 watt-hours) with the flywheel supplying 59 percent of the energy
required and the engine furnishing the remaining 41 percent. These results
imply that for level road operation, it would have been possible to reduce
the engine size roughly 50 percent, with some margin, if it were not neces-
sary to meet EPA/AAPS steady-state design goals for climbing a five percent
grade as discussed earlier.
Consider now the resultant transmission efficiency as a function of vehicle
speed during the full-power transient. Figure C-23 presents these results from
10 to 80 MPH. The lowest efficiency, 78 percent, occurred at approximately
25 MPH where the primary transmission shifts range. Efficiencies above 90 per-
cent were obtained at higher vehicle speeds. As noted earlier, the average
efficiency during the full-power transient was 89.5 percent.
Before presenting a comparison in performance to a conventional system employing
a conventional automatic transmission, the method used to calculate the perfor-
mance of the conventional system under full-power conditions is summarized as
follows. The engine, defined earlier by Figure C-4, was assumed to operate at
maximum horsepower. The automatic transmission under full-power conditions was
in 1st gear from 0 to 25 MPH, 2nd gear from 30 to 55 MPH, and 3rd gear from 60
to 85 MPH. Engine accessory losses were as defined earlier by Figure C-5 and
included air conditioning. The resulting wheel horsepower developed as a func-
tion of steady-state vehicle speed was approximately equivalent to that obtained
for the flywheel/hybrid system during the full-power transient.
The resultant comparison of transmission efficiencies as a function of vehicle
speed is presented by Figure C-24. These results indicate that the conventional
transmission had better full-power efficiency than the flywheel/hybrid trans-
mission at speeds between 15 and 30 MPH and at speeds over 65 MPH. For example,
at 25 MPH the hybrid transmission efficiency was 13 percent lower than the effi-
ciency of a conventional transmission. This lower efficiency, which occurs at
the range switching point, is characteristic of power-splitting transmission and
is similar to the gear-shift points of a conventional transmission.
C-40
-------
100
Vehicle Weight = 5300 Ibs
07, Grade
Engine Accessories Include Air Conditioner
80
Full Power Transient
-t-t-t- -f-f J—
• TH r
•
Transmission Efficiency (Acceleration)
.... i , - I j-H-f
f-f-^-J - M
40 50
Vehicle Speed, MPH
Fig. C-23 Flywheel/Hybrid Transmission Efficiency at Maximum Power
MTI-12544
-------
100
n
i
Conventional Automatic Transmission (Based Upon
Steady State Operation at Maximum Power)
Flywheel/Hybrid Transmission (Based Upon Full
Power Transient with Pierced Flywheel, P = 2.94 psi)
| Vehicle Weight = 5300 Ibs
- . — 0% Grade
Engine Accessories Include Air Conditioner
Transmission Efficiency (Acceleration)
r-f-J-r-'l-1~f t-f-44-f- -r-f-4-r -T~j H-i—H-| ••••"! -,--•
U_Li_L4_U f-14-f ---^4- f • ! I I l-i-4 +4 - '- J-f-* L
pm i t-u; rti [... n T. TillU-lt-I - . -. - -H-..
I i I I T i : 1 1 1 ! ' . TTTl I ! I i n I . . • • I i !
40 50
Vehicle Speed, MPH
Fig. C-24 Comparison of Transmission Efficiencies at Full Power
MTI-12541
-------
At lower pow e r levels, " an ge s wi t c h In g '6 c c u r s at
lower vehicle speeds. For example, ^ader cruise power conditions range switch-
ing occurs at 11 mph. Thus, under normal driving cycle conditions and reduced
power levels the lower efficiency at range switching should be comparable to
the efficiency of SL conventional transmission.
A more important performance comparison is fuel economy. Figure C-25 presents
this comparison. At full power, the advantage of the flywheel/hybrid system is
maximized and this is reflected in the dramatic improvement in miles/gallon
shown by Figure C-25. For example, at 25 mph vehicle speed the hybrid system
fuel economy was approximately 10 MPG compared to 2 MPG for the conventional
system — an improvement of 400 percent even with somewhat lower transmission
efficiency.
Before discussing a comparison of engine operation, it is helpful to consider
some of the operational aspects of the flywheel/hybrid transmission in more
detail during a full-power acceleration from a low vehicle speed. A step
change in the driver's command pedal, initiates the ratio control in the
secondary transmission to decrease,flywheel speed :and the ratio control in the
primary transmission moves to give the maximum possible ratio (torque multi-
plication). Since engine fuel flow is scheduled to produce little engine
power at low speeds (in order to approximate TKE control), the engine fuel
flow is only increasing gradually as a result of the step change in driver pedal.
*
Recalling that the engine and flywheel are linked together by the secondary
transmission ratio control (see Section VI-B), this results in a rapid increase
in engine speed until the error signal in engine speed sensed by the primary
control system starts the primary ratio to decrease. This can be seen by
referring to Figure C-26 which presents the engine speed transient during the
full power transient.
Prior to the transient, the engine was operating at a steady-state speed of
1400 rpm (selected idle during low speed cruise conditions in order to supply
flywheel charging capability). As a result of the step change in pedal, the
engine speed rapidly increased to 3500 rpm and was subsequently regulated by
changing the ratio in the primary transmission at approximately 3200 rpm. Thus,
*This is done to allow flywheel charging as a result of deviations from TKE due
to system losses during deceleration or application of mechanical braking.
C-43
-------
20
18
Vehicle Weight = 5300 Ibs
07. Grade
Engine Accessories Include Air Conditioner
Fuel Density = 6.152 Ib/gal.
16 -4-
,
14
T"
r Flywheel/Hybrid Transmission (Based Upon Full
/Power Transient with Pierced Flywheel, P =2.94 psi)
'Conventional Automatic Transmission (Based Upon
Steady State Operation at Maximum Power)
i I '• ! I i '!"'..
I I I
m
10
20
30 40 50
Vehicle Speed, MPH
60
70
80
90
Fig. C-25 Comparison of Full Power Fuel Economy
tfTI-12543
-------
n
Ul
Step Change in Driver Pedal at t
Vehicle Weight = 5300 Ibs
0% Grade
Pierced Flywheel, P = 2.94 psi
= 0
024 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Time, Seconds
Fig. C-26 Engine Speed Transient During Full Powor Transient
-------
during most of the full power transient, the engine was operating at approxi-
mately a constant speed of 3200 RPM.
As a result, during the initial portions of the full-power transient (at very
low engine power) the engine operated for about 3 seconds at a specific fuel
consumption which was about 50 percent higher than a conventional system at full
power. These results indicate that further improvements in the transmission and
control design will be necessary in order to obtain engine operation at a better
SFC during maximum acceleration. At lower acceleration rates (gradual changes
in the driver pedal), more common to the DREW driving cycle, the engine would
tend to operate close to the minimum SFC operating conditions. As an example,
with output power equivalent to a five percent grade, engine operation at mini-
mum SFC was obtained for all vehicle speeds above 25 MPH.
As mentioned earlier, emission data were not available for the engine specified
by EPA/AAPS. Thus, at this time no conclusion can be made with respect to the
possible reduction in emissions for the flywheel/hybrid propulsion system
during transients with this transmission.
4. Flywheel Charging Analysis
As part of the subject investigation it was of significance to determine what
magnitude of charging times would be expected for the system. In order to
accomplish this, it was assumed that there was a fixed ratio between the engine
speed and the flywheel speed. This would imply that the hydraulic elements
were not taking part in the charging cycle and that the charging was directed
through the gearing with the ring gear held stationary. The inertia of the
flywheel was referred to engine speed and the torque available for acceleration
was determined from the engine performance map which related horsepower and
speed. Knowing torque and reflected inertia, the average rate of accelerating
could be determined. The acceleration and the speed increment were then used
to establish the time required between speed steps.
C-46
-------
The subject calculation was made for charging at minimum SFC as well as charging
at maximum engine horsepower. Two end points of engine speed were also consid-
ered, 3200 and 380C rpm. The key results are summarized below.
TABLE C-2
Flywheel Charging Time
Condition
Min. SFC HP
Min. SFC HP
Max. HP
Max. HP
Engine
Speed
RPM
3200
3800
3200
3800
Time To
Reach Idle
Sec.
2.2
2.2
2.2
2.2
Time-
Idle To
Full
Speed Sec,
42.7
37.7
25.5
22.9
Total
Charge
Time Sec.
44.9
39.9
27.7
25.1
C-47
-------
o
o
3
SECTION D
CONTROLS DESIGN AND ANALYSIS
-------
D. CONTROLS DESIGN AND ANALYSIS
This section presents: 1) an overview of the basic control approach; 2) a review
of the constant total energy control constraint; 3) a discussion of the two
control approaches considered; and 4) a detailed description of the implementa-
tion and operation of the selected control approach. Additional detailed analy-
sis of-the1 control'-'system is contained in 'Appendix II ViiS't'ab^lity' andi Analog. •
.Computer Simulation Analyses.
1. Basic Control Approach
The basic interrelationships of the engine, flywheel, transmission and vehicle
are indicated in the block diagram of Figure D-l. The power paths of the engine,
flywheel and vehicle are interconnected through the transmission. Allocating
and directing of system power flow is established by the controls, which accept
acceleration, deceleration and modal commands from the operator; engine, fly-
wheel and output speed signals from the system; and provide throttle and ratio
commands to the engine and transmission, respectively.
The overall transmission consists of two separately controlled split-path
hydrostatic links: the Primary path, which establishes a given ratio between
the engine and vehicle for optimum torque-speed loading condition of the engine
in the steady-state; and the Secondary path, which controls the direction and
magnitude of power flow to and from the flywheel during vehicle velocity
transients.
2. Constant Total Energy Constraint
As pointed out by LMSC (2 ), it is advantageous to maintain the flywheel charge
by following the requirement that the total kinetic energy (TKE) of the system
remains constant. In other words, the kinetic energy of the flywheel plus the
kinetic energy of the vehicle equals a constant. This relationship is shown
graphically in Figure D-2.
'! -I
-------
FLYWHEEL
ENGINE
Engine
Output
*
Throttle
Command
Flywheel
Output
Transmission
Output
TRANSMISSION
}
Primary
Transmission
Conmaod
Engine
_Speed
N>
Accel • Pedal
Selector T-*
Brake
1
I
Secondary '
Transmission |
Command I
r— '
Output
I Speed
CONTROLS
^
Vehicle
Velocity
VEHICLE
Flywheel
Speed
—— ^— -^ Link Dependent on Detailed System Form
Fig. D-l System and Controls Interrelationships
-------
MAX
u
o
r-l
-------
As indicated by the locus curve of Figure D-2, the maintenance of a constant
TKE level implies that the flywheel velocity ( hence, the "state of charge")
will be maximum when the vehicle is stopped, and at its specified minimum when
the vehicle is at its specified maximum velocity. Considered as an energy
storage element, the flywheel has the highest charge level when the vehicle is
in most need of energy for acceleration, and conversely is in best condition
to accept energy from the vehicle for deceleration when the vehicle velocity
(hence, charge) is highest.
To the extent that a constant TKE value is maintained on an instantaneous basis,
the energy utilization and storage action of the system is constant and indepen-
dent of load conditions and immediate past history.
In an ideal case where the road is horizontal and all losses (including those
due to the transmission and dissipative braking) are zero, total system kinetic
energy would inherently be preserved. Energy would be transferred back and
forth between the flywheel and vehicle, and only the rate of transfer (hence,
accel-decel rate of the vehicle) would be of concern.
In the real case, observation of the TKE constraint is complicated by factors
such as:
(1) hills — which can introduce significant unscheduled system kinetic
energy variations due to potential energy variations,
(2) dissipative braking - which can introduce rapid and significant
unscheduled changes in system TKE level, and
(3) variable loading — as by the number of passengers and/or trunk load
carried, or in pulling trailing vehicles, which can significantly
alter the value of vehicle mass used in computing and implementing
the TKE control scheme.
3. Control Approaches Considered
Two basic approaches to maintaining constant TKE were considered: one involving
the measuring and utilization of vehicle velocity in an attempt to maintain
system TKE by closed-loop feedback control techniques; and the second using an
approximated value for vehicle velocity based upon driver pedal position in
D-4
-------
an open loop scheduled manner.
Functional block diagrams for the two basic types of TKE control are shown in
Figures D-3 and D-4, respectively.
The major basic difference between the two control configurations is the method
of deriving a vehicle velocity value for controlling system total kinetic energy.
The closed-loop (Type A) control of Figure D-3 uses a speed governor for measur-
ing output shaft: (hence, vehicle) speed. In the open-loop scheduled (Type B)
control, output speed is approximated from pedal position by a '-cam-generated
schedule.
The Type A configuration (Figure D-3) constitutes closed-loop control of TKE
since actual vehicle velocity feedback is used, allowing a continuous comparison
of flywheel and vehicle velocities to be made.
2 2
Due to the nature of the TKE computation (TKE = 1/2 Jp Nf + 1/2 MV v ) , the
vehicle speed feedback is positive (regenerative) in that an increase in
vehicle speed commands a decrease in flywheel speed, which in turn results in
a further increase in vehicle speed.
It is important to point out that whenever wheel slip occurs, such as vehicle
operation on road ice, these regenerative control effects could result in
difficult driver control situations. Also, with this type of control approach,
a destabilizing feel can occur when climbing or descending hills. In other
words, as the vehicle proceeds down a hill, the resultant increase in vehicle
velocity commands the flywheel to accelerate the vehicle. This situation
would be disturbing to the driver.
Although control systems can be implemented with positive feedback loops, the
magnitude of gain must be carefully restricted to be less than unity to prevent
regenerative behavior. If gain is equal to or greater than unity, the system
will be unstable in that, once the output is started in motion,it will continue
to move until system saturation occurs, even without an input to the control
loop. If the gain is too low, system transient response will be too slow and
general performance poor. Thus, in principle there is little range for adjusting
D-5
-------
RATE
VALVE
HRAKE
Accelerator
Pedal
SECONDARY
CONTROL
SECONDARY
TRANSMISSION
KATE
VALVE
v
ENGINE
ENGINE
GOVERNOR
OUTPUT
GOVERNOR
PRIMARY
TRANSMISSION
PRIMARY
CONTROL
Fig. D-3 Closed-Loop TKE Control (Type A)
BRA£E
PEDAL
FLYWHEEL
GOVERNOR
SECONDARY
TRANSMISSION
ACCELERATOR
PEDAL
ENGINE
GOVERNOR
PRIMARY
TRANSMISSION
PRIMARY
CONTROL
Fig. D-4 Open-Loop Scheduled TKE Control (Type B)
D-6
MTI-12527
-------
the gain for performance considerations, from an implementation standpoint,
gain variations can result in inadvertafit regeneration with a resultant loss of
control.
In the Type A TKE control, the sensitivity to gain normally experienced with
positive feedback is complicated by the fact that the feedback velocity function
is actually the square of velocity as required to follow the kinetic energy
equation. This means that the effective feedback gain increases with vehicle
velocity (is proportional to it) and,for stability, the gain must be restricted
to less than unity at the highest velocity and allowed to degrade at lower
velocities - resulting in significant variations in response with velocity.
As indicated by the curve of Figure D-2, the TKE equation as implemented by
the Type A approach merely prescribes the locus of flywheel and vehicle velocity
pairs for a given constant TKE value. The rate valves shown in Figure D-3 are
required to provide transient signals to the secondary (flywheel) transmission
to establish and direct the rate of energy flow to and from the flywheel for
vehicle acceleration and dynamic braking.
With the Type B open-loop control approach (Figure D-4) the vehicle "kinetic
energy" input for the TKE control function has the form of a well-defined
command rather than an instantaneous feedback signal — eliminating the positive
feedback effect inherent in the Type A approach. System gains can therefore
be varied over a wider range to optimize performance and stability; and normal
gain variations will not result in instability or loss of control. Also, the
driver pedal tends to act like a torque command for the propulsion system
which is analogous to present automotive systems.
As previously mentioned, the regenerative effect of the Type A approach would
cause a destabilizing feel to hill climbing and descending; however, with the
Type B control hills would not result in the flywheel influencing vehicle .speed
unless the driver commands it to.
As shown in Figure D-4, the Type B control is programmed by a^cariKdrdverayby the
accelerator pedal to provide a signal proportional to vehicle kinetic energy
at specific values of grade, vehicle mass, wind load, friction, and engine
D-7
-------
condition. A change in any of these pardiucters could cause the vehicle speed
and thus the vehicle kinetic energy to be different from the programmed value.
Thus, some compromise or selection of nominal condition is required in order
to establish the optimum open loop schedule. This is illustrated by Figufe D-5
where the schedule was selected to provide constant TKE at zero grade. Operation
at five percent grade conditions then results in lower flywheel speeds at the
same vehicle velocity under steady-state conditions.
Figure D-6 shows the possible variation of TKE at different vehicle speeds due
to the effect of changing vehicle mass and grade conditions. These results
clearly indicate that as the load torque increases, the driver will have less
available torque to accelerate the vehicle. A situation similar to that
encountered with conventional propulsion systems.
Figure D-7 shows the change in flywheel speed which occurs in going up or down
a hill, at constant vehicle speed with the Type B control. Flywheel speed
decreases when going up a hill, thus providing some power for climbing the hill.
Flywheel speed increases when going down a hill, thus transferring part of the
vehicle potential to the flywheel. One of the significant advantages of the
Type B control configuration is the use of flywheel power to aid in climbing
short hills. Of course, the total kinetic energy will, not remain constant
during hill climbing. Upon reaching the top of a hill, the flywheel speed will
be low. The accelerator pedal must be depressed farther, at a given vehicle
speed, to provide power for accelerating the flywheel. After the flywheel is
charged, the accelerator pedal can be returned to the normal position.
Upon reaching the bottom of a hill, the flywheel speed will be high. Therefore,
dynamic braking cannot be used until the flywheel returns to the normal speed.
If a stop must be made at the bottom of a hill, the brake pedal must be depressed
far enough to engage the mechanical brakes. There will be a difference in brake
feel under this condition. It should be possible to maintain constant brake
pedal feeling by adding compensation to the brake pedal. However, this would
add to the control complexity. Upon coming to a stop, flywheel speed will be
at the correct value. An overspeed limiter prevents the flywheel from acceler-
ating to a higher speed.
D-8
-------
25,000
20,000
TJ
01
0)
a
CO
01
01
15,000
10,000
()I Grade (Constant
Total Kinetic Energy)
100
Vehicle Velocity, Miles Per Hour
Fig. D-5 Flywheel Speed Versua Vehicle Velocity
Type B Open Valve Control
D-9
-------
1.2
1.0
0.8
"O
01
•H
m
01
O
0.6
0.4
0.2
0
10% Increase in Vehicle Mass at 0% Grade
•Minimum Flywheel
Speed
Note: Changes in wind load, fric-
tion, and engine conditions
have effect similar to
change in grade.
20 40 60
Vehicle Speed, Miles Per Hour
80
100
Fig. D-6
Effect on TKE of Varying Vehicle Mass and
Grade Conditions - Type B Open-Loop Control
D-10
MTI-12499
-------
ALTITUDE
HILL
STEEPER
HILL
ACCELERATOR
PEDAL
/V
LJ
BRAKE
PECAL
BRAKE
APPLIED
VEHICLE
VELOCITY
CONSTANT VEHICLE SPEED
FLYWHEEL
SPEED
TIME
Fig. D-7 Effect of Hills on Flywheel Speed at Constant Vehicle Speed
D-ll
-------
On a comparative basis, although the Type * TKE control is initially attractive
because it would monitor vehicle velocity and would therefore utilize an accurately
computed value of kinetic energy, the Type B approach was selected for final
design evaluation and costing on the following major bases:
(1) Control System Complexity and Cost
The Type B approach is inherently less costly by virtue of eliminating the
output speed sensor and the brake and accelerator rate valves. Although the
detailed dynamic signal shaping techniques were not finalized for either
Type A or Type B approaches, within the scope of the study, the Type B
requirements appear to be-.basically, simpler because of the inherent better
stability of that approach.
(2) General Performance and Feel
Assuming the Type A approach is compensated appropriately to achieve acceptable
stability, the steady-state TKE performance of the Type A and B systems would
be similar for horizontal driving conditions. As indicated previously, the
Type A approach increases driver control requirements on hills and icy roads,
and it eliminates the possibility of using the flywheel (assuming no TKE
error) either to provide energy in climbing or to store energy on descending
a hill. At some departure from TKE, the Type B approach provides the capability
for the flywheel to provide energy during hill climbing and to store energy
(as desired) when on descending hills. Also, the Type B control tends to make
the driver pedal a torque command to the system.
D-12
-------
4. Implementation and Operation of the Type B Open-Loop Control System
General Description
A simplified system diagram is illustrated in Figure D-8. The inputs to the
system are the same as those of the typical family car; selector lever position
(plus a position for initially charging the flywheel), accelerator pedal position,
and brake pedal position. The control variables are the hear, engine throttle
position, and the continuously variable ratios of the two transmissions. Feed-
back signals are engine speed and flywheel speed.
Acceleration
A step change in accelerator pedal position in the direction to increase vehicle
speed results in three inputs to the control system. The first input acts
through the primary control system to command a new steady-state engine speed.
The second input acts through the secondary control system to effectively vary
the secondary transmission ratio between the flywheel and engine speed. Fuel
flow to the engine is modulated by the third input providing engine power
approximately equal to the steady-state losses at each speed.
Varying the secondary transmission ratio results in a decelerating torque being
applied to the flywheel and an accelerating torque applied to the engine shaft.
The engine speed increases to the commanded steady-state value and is held at
this speed by the primary transmission ratio being varied with changes in load
through action of the primary transmission controls.
Kinetic energy is transferred from the flywheel to the vehicle with vehicle
acceleration resulting.
Dynamic compensation is used to maintain the correct sequence and rates between
the control functions.
Deceleration
When the accelerator pedal is returned to the idle position at high vehicle
speed, the vehicle speed decreases slowly in the same manner as a conventional
vehicle. Depressing the brake pedal part way varies the secondary transmission
ratio to transfer kinetic energy from the vehicle to the flywheel — thereby
using dynamic braking for decelerating the vehicle. Depressing the brake pedal
farther engages the mechanical brakes for faster deceleration.
D-13
-------
Mechanical
Brake
Flywheel
Governor
Flywheel
Brake Pedal
Accelerator
Pedal
Selector Lever
Secondary
Control
Secondary
Transmission
j—»• CAM
v2 (scheduled)
—•*
Engine
Engine
Governor
Modal
Control
Primary
Transmissior
-ft
1
Primary
Control
Fig. D-8 Basic System Functional Diagram
D-14
-------
Fast Stop
The reduction of engine speed when the vehicle is brought to a stop results in
disengagement of the primary transmission. The secondary transmission normally
remains engaged.
The flywheel speed will be approximately correct when the vehicle stops due to
dynamic braking only. After a fast stop in which the mechanical brakes are
applied, the flywheel speed will be low. The secondary control:system then
causes the flywheel to slowly accelerate to the correct speed at a rate within
the power capability of the engine at idle.
Total Kinetic Energy Behavior
The secondary control system is programmed to vary the flywheel speed to main-
tain the total system kinetic energy (flywheel plus vehicle) at a constant value
for zero grade nominal load conditions. Variations of grade, load and engine
condition can cause variation of the total kinetic energy.
Implementation and Operation
A control component diagram and hardware implementation schematic are shown in
Figures D-9 and D-10.
The manual shift lever is used to select the operating mode. The shift pattern
schematic as shown below follows the present day automobile shift pattern as
closely as practical.
5 R C I
1 i i
1 i 1
« D 2 1
P - Park
R - Reverse
C - Charge
N - Neutral
D - Drive
2 - Second
1 - Low
D-15
-------
SECONDARY CONTROLS
O
i
Secondary
Cam Plates
Mechanlca1
Path
Hydraulic
Path
Primary
Transmission
1
i
»
Engine
Engage
Governor
High
Range
Clutch
Low Range
Clutch
Accel.
Pedal
Engine
Dynamic
Compensator
-\
\
«
Flywheel
Charge
Piston
\
Control
Cam
*
Cover
Cam
1
Engage
Valve
i
h. f
fcj
, 1
i
»
Primary
Piston
Actuator
i
i
Regulator
Governor
i
*
1
Control
Cam
\
^
Governor
Cam
PRIMARY CONTROLS
W
Fig.' D-9 Flywheel/Hybrid Transmission — Control Component Diagram
MTI-12536
-------
o
I
Fig. D-10 Control System - Hardware Implementation Schematic
KII-12522
-------
Control Valves 1 and 2, which are positioned by the shift lever, direct pressures
to the control elements as required in'each mode.
In the charge mode, the primary transmission and high-range clutch are disen-
gaged. The kinetic energy summing valve provides a pressure proportional to
kinetic energy error which acts on the flywheel charge piston to move the
throttle. Thus, the engine speeds up to charge the flywheel. When the flywheel
is fully charged, kinetic energy error is zero and the engine slows down to
idle speed. The secondary engage valve is actuated at an engine speed of 900
to 1100 rpm, providing pressure to hydrostatic elements III and IV, thus en-
gaging the secondary transmission. The secondary transmission remains engaged
for all shift lever positions as long as engine speed is above approximately
900 rpm.
In neutral, pressure is directed by Control Valve 1 to the primary piston actua-
tor to move the sleeve to the position which limits piston stroke. Pressure is
transmitted through the shuttle valve to engage the low-range brake. The engage
valve is in the open position, and the swashplate of Element I is near zero dis-
placement which allows this element to rotate freely to effect zero output
torque. A cam driven by the shift lever sets the engine regulator governor bias
load to overcome the flyweight force, thus moving the governor valve. The re-
sultant position of the governor valve provides flow to the primary actuator
which moves the piston to the maximum torque position C. Accordingly, in neutral,
the control system presets the primary swashplate and low-range brake for low
ratio output for initial vehicle acceleration from a stopped position.
When the control valves are shifted to the drive position, the fluid pressure
connections to the low-range brake and high-range clutch remain the same as
in the neutral position. Pressure from the engage governor is transmitted
through Control Valve 2 to the primary and secondary engage valves. The output
pressure from the engage governor increases as engine speed increases. This
pressure acts on the primary and secondary engage valves to engage the secondary
transmission at 900 to 1100 rpm engine speed and to engage the primary trans-
mission at 1200 to 1400 rpm engine speed.
D-18
-------
During drive operation the engine xemulator governor controls hydraulic flow
to the opposite sides of the primary actuator piston to effect movement of
the Element I swashplate. The movement of the governor valve is regulated in
part by the position of the cam which adjusts the speed setting as a function
of the accelerator pedal position. Accordingly, for every throttle position,
the governor valve mechanism continuously controls the position of the primary
actuator piston to vary the operating ratio to maintain a set engine speed.
This provides a means for ideally matching the engine and vehicle speeds as a
function of throttle position to provide optimum engine performance for mini-
mizing emissions.
It will be noted that in initially accelerating, the clutch and brake valve
rides upon the upper surface of the control cam, thereby providing fluid
pressure, through the shuttle valve, to engage the low-range brake. When the
primary transmission output speed increases, movement of the cam causes the
clutch and brake valve to move down to the lower surface of the cam. In the
extended position of this valve, the fluid pressure to the low-range brake is
vented, thereby releasing the low-range brake. Also, when this valve is
extended, fluid pressure is provided to the high-range clutch, thereby engaging
this clutch. This transition is made while both the high-range clutch and
low-range brake are in synchronization to effect very smooth operation. This,
in addition to non-power shift of both the clutch and brake, provides wear-free
operation.
In Modes 2 and 1, the control cam introduces a bias to the engine regulator
governor which varies the engine speed setpoint at which the primary transmission
switches from low to high range.
In reverse, fluid pressure is transmitted from Control Valve 1, through the
shuttle valve, to engage the low-range brake. The control cam is positioned
by the mode selector to provide additional force on the engine regulator gover-
nor spring thus moving the engine regulator governor valve downward, and pro-
viding fluid pressure to the bottom of the primary piston actuator. Pressure
in the top chamber of the primary actuator is vented through Control Valve 1.
Thus, the piston and sleeve of the primary actuator both move to the top
position. The additional stroke of the cam plate due to movement of the
D-19
-------
sleeve causes the pin connected with the swashplate housing to move into the
negative angle portion of the cam slot, thereby positioning Element I swashplate
at a negative angle for reverse output.
It will be noted that, when Control Valve I is moved to the reverse position,
fluid pressure is directed to the primary engage valve so as to engage the
primary hydrostatic transmission.
Park, which opens the engage valve to bypass fluid around the hydraulic motor
and pump;(Elements I and II) permits the engine to idle without transmitting
any torque to the transmission output shaft. The engine idlds below 1200 rpm.
In addition the parking lock is positioned to lock the transmission output shaft
to the rear wheels.
The secondary transmission and control system continuously vary the ratio
between the engine and flywheel to maintain a nominal constant total kinetic
energy. The kinetic energy summing valve provides an output pressure propor-
tional to kinetic energy error, which acts on the secondary piston actuator to
vary the swashplate angles of hydrostatic Elements III and IV, thus varying
the ratio.
Each position of the accelerator pedal, at constant grade and road load,
corresponds to a steady-state vehicle velocity, and therefore to a scheduled
vehicle kinetic energy. A cam driven by the accelerator pedal varies the
load on the kinetic energy summing valve spring in proportion to the commanded
value of vehicle kinetic energy. The spring preload is proportional to the
desired value of total kinetic energy. The flywheel governor, which is driven
by the flywheel through a 6 to 1 reduction ratio, provides a force proportional
to flywheel kinetic energy. This force is applied to the kinetic energy
summing valve through a coupling spring.
At zero accelerator pedal position, the kinetic energy summing valve spring
applies the maximum load to the flywheel speed governor valve. A cam causes
this spring force to decrease as the accelerator pedal is depressed. At any
accelerator pedal position, if the flywheel speed is too low, the kinetic energy
summing valve spring forces the governor valve downward. High pressure is then
D-20
-------
directed to the bottom of the secondary piston actuator, and the top is vented.
The secondary piston actuator then moves the swashplates in the direction to
increase the ratio of flywheel to engine speed, thus increasing flywheel speed.
When the flywheel speed reaches the desired value, the flywheel governor force
equals the kinetic energy summing valve spring force. The governor valve then
moves to the neutral position and the actuator motion ceases. If flywheel
speed is too high, the governor flyweight force moves the governor valve
upward, thus providing flow to move the actuator as required to decrease
flywheel speed.
Pressure feedback from the secondary actuator to the kinetic energy summing
valve is used to reduce the phase lag of the actuator as required for stable
operation. The pressure feedback also reduces the effect of engine speed on
the secondary control system. A further advantage of the pressure feedback
is that torque applied to the flywheel becomes proportional to kinetic energy
error.
The flywheel dynamic compensator is used to limit the secondary piston actuator
velocity as required to obtain fast acceleration without saturating the secondary
pressure.
The hydrostatic transmission relief valves, which are located in the primary
and secondary engage valve housings, are set at approximately 3600 psi. The
control system should hold the pressures below 3000 psi during normal operation
for maximum efficiency and minimum wear. Pressure surges are held below the
relief valve settings, during normal operation, by the primary actuator rate
limits, and by the engine dynamic compensator and flywheel dynamic compensator.
D-21
-------
o
o
SECTION E
COST ANALYSIS
-------
E. COST ANALYSIS
Described in this section is the method employed to determine transmission costs
and a discussion of the results is included. The cost data presented was based
on the experience of automotive cost consultants based upon cost information and
practices of the Ford Motor Company. Therefore, this procedure provides a sound
approach to comparing the cost of the flywheel-hybrid transmission with that of
the standard multispeed torque converter (automatic) transmission.
The objectives of the cost analysis were to determine the original equipment
manufacturercost (O.E.M) for production quantities of 100,000 and 1,000,000
units per year of the flywheel-hybrid transmission and then compare that cost to
similar costs for a multispeed (automatic) transmission.
Feasible Transmission Concept Cost
During the initial feasibility analysis, seven transmission concepts were iden-
tified as possible candidates and sketch layouts were drawn. Estimates of the
O.E.M. costs for these transmission concepts were made and referenced against
the automatic transmission used on current medium sized vehicles. The results
are presented in Table E-l.
The power-splitting transmission was selected from the seven candidates as the
type of transmission required to accommodate the dual power path propulsion
system. Estimates of the final cost ratios were made and are presented in
Table E-2.
The method of establishing the information presented is discussed in the follow-
ing paragraphs. Preliminary cost ratios did not have the depth of analysis as
did the final ratios and were, as a result, optimistic. Since the same optimism
prevailed throughout the analysis of the seven candidates, the ratios of
Table E-l were on a consistent basis and adequate for the purpose that of
assessing the cost category for the intial screening task.
E-l
-------
TABLE E-l
Preliminary Transmission Cost Analysis - Ratios
1,000,000 Units Per Year
O.E.M. Cost
100,000 Units Per Year '•
O.E.M. Cost !
SK-J-4258
3 Element
Hydrodynamic
SK-E-4260
2 Element
Hydrodynamic
SK-J-4257
Hydrostatic
SK-E-4256
Power Split
SK-E-4261
Power Split
(Offset)
SK-D-4259
Hydrodynamic
Hydrostatic
SK-A-4262
Hydrodynamic
2 Coupling
Standard
Multi-Speed
Torque Converter
("Automatic")
1.9
1.5
2.1
1.9
2.0
1.9
1.7
2.45
1.94
2.71
2.48
2.58
2.48
2.19
1.0
1.29
K-2
-------
TABLE E-2 FINAL TRANSMISSION COST ANALYSIS RATIOS
Standard
Multi-Speed Torque
Converter ("Automatic")
Transmission for
Medium Size Vehicle
Power
Splitting Transmission
for Flywheel/Heat
Engine Medium Size
Vehicle (Inline Flywheel)
Power Splitting
Transmission for
Flywheel/Heat Engine Medium
Size Vehicle (Offset Flywheel)
1) Variable Cost Ratio
2) O.E.M. Cost Ratio
3) Control Variable Cost Ratio
4) Labor Content Ratio
5) Material Content Ratio
A
1.00
1.00
1.00
1.00
1.00
B
1.19
1.15-1.25
1.19
1.00
1.20
C
1.29
1.25-1.35
1.29
1.50
1.20
A
2.40
2.25-2.35
2.87
2.13
2.65
B
2.85
2.70-2.80
3.41
2.13
3.18
C
3.10
2.95-3.05
3.70
3.19
3.18
A
2.53
2.35-2.45
2.87
2.25
2.79
B
3.01
2.85-2.95
3.41
2.25
3.35
C
3.26
3.10-3.20
3.70
3.37
3.35
A) Ratios based on manufacture of 1,000,000 units per year
3) Ratios based on manufacture of 100,000 units per year with tooling as for 1,000,000 units
c) Ratios based on manufacture of 100,000 units per year with tooling suitable for maximum yearly
manufacture of 100,000 units.
-------
Although not shown on the transmission concept sketches, cost saving design
improvements suggested by the automotive consultants were factored into the
finalized cost ratios.
Costing Procedures
The technique for obtaining the costs for the power-splitting transmission is
outlined and a sample sheet ia included as Table E-3. It was necesary to re-
view a total of 390 items to obtain a valid cost comparison. The few examples
presented on the sample sheet were, in most instances, selected to present the
costs of the hydraulic components peculiar to the power-splitting transmission.
The package drawing, SK-E-4283 (Figure A-12, pp. A-22 to .A-2&), was;used to identify
the items for costing. Components, such as the hydrostatic pumps and motors —
not normally found in an automobile transmission, were detailed with sufficient
dimensional and material information for an accurate cost estimate. The approach
is similar to that used by high volume car manufacturers and is discussed in
the following paragraphs.
The initial column of Table E-3 describes the part or function to be costed.
Columns 2 and 3 are the part number and number of such parts called out on
the transmission parts list.
Column 4 presents the method of manufacturing the part as established by the
automotive company.
In Column 5 the material costs were established, and they include all costs
to bring the part to the "as-purchased" condition. For example, a die cast
component would have rough weight established to develop material cost. The
material cost was the actual purchase price in the "as-purchased" condition.
The "in-house" manufacturing costs to finish a specific part are developed on
an extension of variable minute costs times labor minute content. Variable
minute costs include direct labor, indirect labor and non-variable burden.
E-4
-------
TABLE C-3 COST SAMPLE SHEET
DESCRIPTION
Shaft, Element I
Cylinder Block - Primary Transmission
Pl3t°" — — ^ — anSm
Trunnion - Swashplate - Prl .
Support - Swashplate - Pri .
Swashplate - Motor- Pump - Prl .
Planet Gear - Fly, Planetary
RlnR Gear - Fly. Planetary
Gear - Element III - Fly. Planetary
Plnnptflry Aiiy Flywheel
Governor - Eneaee - Flywheel
TKE Valve and Governor Assy
NOMENCLATURE
TOTAL PER ASS'Y REMARKS
ITEM
NO.
4
8
11
12
13
26
26
23
--
--
QTY
i
2
1
1
2
3
1
1
1
1
P.P.
P.R.
P.S./F
M
A
MAKE
BUY
PR
PR
PR
PR
PF
M
PR
RR
PF
PF
Pur
Pur
Pur
Mar
As;
MAT'L
COST (D
1 .120
2.440
1 .510
.900
4.800
.810
1.860
.581
1.611
6.717
chased as
chased In
chased as
u fa c cured
emble
DLLARS)
finished
rough cc
o semi-f
in house
LABOR
MIN.
9.70
18.00
12.00
7.02
5.70
8.30
6.30
10.25
22.50
(tern
ndltlon ,
Lnished 1
such as c
tern
LABOR
COST
fVARUD
1 .693
3.140
2.094
1 .225
.995
1.448
I .099
1.789
3.933
istlng, o
1LLARS)
d forRin
TOTAL
COST(DO
2.813
5.580
3.604
2. 125
4.800
1.805
3.308
1.679
3.400
10.650
s
.LARS)
FOFR
Mech
Nodu
Cast
Heav
Stl.
Heat
ForR
nR - AIS
nite Cas
ar Iron
Iron
' Coined
Bar
Treat No
ng - AIS
^ n0t SP
8620 St
Ing (She
H.T.) (P
itpR. for
lular Iro
[ 8620 St
el
1 Mold)
a r 1. Ha 1 L
Blank pe
>el
"
<
(
(
(
Torr. (
(
(
(
(
<
ost Sht
ost Sht
ost Sht 1
ost Sht 1
ost Sht 1
ost Sht 2
;ost Sht
lost Sht
ost Sht7
xist Sht 1
-------
In Column 6, the actual "in-house" number of labor minutes to complete the manu-
facturing task were listed and in Column 7 the variable minute costs were listed,
Column 8 is the total cost dollars for each item or task labeled in Column 2.
The study was based on variable costs and not O.E.M. costs. The O.E.M. or
transfer costs would include cost allocations for fixed burden, scrap, factory
cost adjustments, general and administrative costs, profit and capital invest-
ment. Capital investment would include costs for facilities, tooling and engin-
eering expense. Since many of these transfer costs would vary with different
automotive companies, the O.E.M. data were not as basic as the variable cost
data, and; therefore, were not considered as reliable when comparing information
from different sources.
In addition, transfer costs for facilities would not reflect the same in the
transmission cost ratios. For instance, the cost of the facilities for the
automatic and power-splitting transmissions could be the same.
As an example, let:
1.0 = Variable costs of automatic transmission
2.0 = Variable costs of power-splitting transmission
0.1 = Facilities costs for either transmission.
2.0
Variable cost ratio without facilities included = -H-r = 2.0
2.1
O.E.M. or cost ratio with facilities included = T^T = 1.9
J. • J.
Therefore, when dealing with ratios the increased cost of the basic transmission
is not correctly identified if only the O.E.M. cost ratios were presented.
The cost analysis task dealt in ratios because the actual variable dollar cost
of an automatic transmission was automotive company proprietary information.
E-7
-------
The range in the O.E.M. ratios provided in Table E-2 account for the possible
variances associated with the costs.
The cost estimates are presented in Tables E-l and E-2 as a ratio of hybrid
propulsion system transmission costs to conventional automatic transmission
costs for a medium-size car line.
All ratios represent the cost of the item being considered divided by the cost
of a multi-speed torque converter ("automatic") transmission for medium-size
vehicles as now produced in quantity by automotive manufacturers.
The detailed cost study was made for 1,000,000 units per year volume of both
standard automatic and power-splitting transmissions. A second estimate for
the manufacture of 100,000 units per year volume was presented. This estimate
assumes the same tooling and facilities as for the 1,000,000 units per year
volume. Essentially it reflects the increase in purchase costs when the volume
is reduced.
A third estimate for the manufacture of 100,000 units per year volume was pre-
sented. This estimate uses tooling and facilities suitable for the manufacture
of 100,000 units per year with no increase, in production predicted for the fu-
ture. This number represents the increase in purchase material costs and labor
content costs.
As shown in Table E-2, the ratio of the variable costs for the power-splitting
to that of the multi-speed converter transmission was 2.40 — an increase of
140 per cent. Primarily, two factors were responsible for the increased cost:
1. In reality, the power-splitting transmission was designed to accept
power from two separate propulsion sources. Such a feat required that
the components of two transmissions be packaged as one. Therefore, the
costs reflect the major torque transfer elements of two transmissions.
F.-8
-------
2. The control required to properly relate the heat engine, flywheel,
heat engine transmission and flywheel transmission has essentially
two times the number of components as the standard transmission control.
Also in Table E-2 the control variable cost ratio has been presented. The ratio
of 2.87 or an increase of 187 percent in costs reflects the complexity of pro-
viding controls for such a propulsion system.
Finally, the labor content ratio and material content ratio are given to es-
tablish the area of the major portion of the increased cost. Since the power-
splitting type has the torque elements of two transmissions, the increase in
material costs was the major contributor to the high cost ratio.
Included as part of Table E-2 are the cost ratios for a power-splitting trans-
mission with an offset flywheel. The increased values reflect the additional
gear shafts needed to offset the flywheel. Again the material content contrib-
uted the major portion of the cost increase.
In summary, the hybrid propulsion system transmission requires twice the num-
ber of torque transmitting components and the control components resulting in
a cost of 2.40 times that of the standard automatic transmission.
One additional cost comparison was investigated. This was a determination of
the ratio of the costs of the smaller engine plus the inline pierced flywheel
plus the power-splitting transmission divided by the costs of the large engine plus
the standard automatic transmission. Costs were based on the production of
1,000,000 units per year. The ratio was 1.63.
If the non-pierced flywheel is used, the cost ratio is 1.69.
Therefore, the hybrid propulsion system would cost approximately 60 to 70
percent more than the system presently installed in automobiles.
E-9
-------
SECTION F
SAFETY ANALYSIS
9!.
-------
F. SAFETY ANALYSIS
The approach for evaluating potential safety problems with the heat engine/fly-
wheel hybrid transmission was to look initially at the main assemblies and how
they would influence operation in the event of a malfunction or failure. Using
this approach, we found that the basic operation would fall into two categories:
1) a loss of performance which would be similar to what would happen with a
standard transmission, that is, loss of power to the road and requirement that
the automobile would have to be driven to the shoulder and repair would be
required; 2) a behavior which might be startling to the driver which would be
classed as malfunctions which result in a pathological effect.
Transmission Elements
Rather than dwell on what we might term as standard failures, Table F-l sum-
marizes the malfunctions and the effects as determined by the first review.
These are identified in accordance with the transmission schematic in Figure B-l.
However, noted in Table F-l, are three specific failures in the transmission
which fall into the pathological category and which could result in significant
safety hazards unless some corrective means was incorporated into the design.
In general, these latter types of failures are associated with the fact that
the flywheel is a separate source of power which in the event of malfunction
can operate in an unexpected and uncontrolled fashion. The three failures in
this category are as follows:
1. Lockup of the Output Planetary B
The effect would be to rapidly change the gear ratio between the flywheel
and output shaft such that a rapid change of output speed would be
realized. For example, during this type of failure, the vehicle may
accelerate without driver command. Generally speaking, this type of
problem will be of short duration. However, it would present a signi-
ficant surprise and probably a pathological reaction.
F-l
-------
TABLE F-l
TRANSMISSION FAILURE ANALSIS SUMMARY
TRANSMISSION
COMPONENT
TYPE
OF FAILURE
EXAMPLE
OF FAILURE
EFFECT
CORRECTIVE ACTION
Primary
Hydrostatic
(Elements I &
ID
Clutch & Brake
Interlock Sys-
tem for Clutch
and Brake
Lockup
Free Wheeling
Fixed Ratio
Open or Closed
Open or Closed
Bearing Seizure
Loss of Hydraulic
Pressure. Mode
Switch
Trunnion Bearing
Failure
Actuator Failure
Valve Seizure
Lock rear wheels with
probable slip of brake
and clutch.
Gradual vehicle decelera-
tion.
Engine stall.
Flywheel overdrives Ele-
ment III with subsequent
opening of pressure relief
valve.
Loss of drive torque,
Vehicle slows.
Loss of variable speed
control with subsequent
engine stall.
Abnormal high or low
range operation.
Abnormal high or low
range operation.
Set slip level for clutch
and brake.
Size relief for required
flow.
Use interlock system.
-------
TABLE F-l (cont.)
TRANSMISSION FAILURE ANALYSIS SUMMARY
TRANSMISSION
COMPONENT
TYPE
OF FAILURE
EXAMPLE
OF FAILURE
EFFECT
CORRECTIVE ACTION
Secondary
Hydrostatic
Element III*
Element IV
Element III.
and/or IV
Output
Planetaries
Planetary B*
Planetary B
Planetary C
Freeze Up or
Lockup
Freeze Up or
Lockup
Free Wheeling
Lockup
Free Wheeling
Lockup
Free Wheeling
Bearing Failure
Bearing Failure
Sheared Shaft or
Loss of Hydraulic
Pressure Mode
Switch
Bearing or Gear
Failure (Freeze
Up)
Sheared or Frac-
tured Shaft.
Bearing Seizure
Loss of Gear Teeth
Change of vehicle speed.
Possible flywheel over-
speed.
No output. Engine stalls,
Same as Planetary "A"
lockup.
Loss of Planetary "A"
reaction and loss of fly-
wheel power.
Rapid change of vehicle
speed, + or —, depending
on range condition.
Engine stall.
Loss of output power,
Slip of low-range brake
with gradual loss of
vehicle speed.
No low range power.
Hydraulic dump output of
Element III.
Containment or growth ring.
Shear joint or override
mechanism.
-------
TABLE F-l (cont.)
TRANSMISSION FAILURE ANALYSIS SUMMARY
TRANSMISSION
COMPONENT
TYPE
OF FAILURE
EXAMPLE
OF FAILURE
EFFECT
CORRECTIVE ACTION
Input Planetary
Planetary A*
Planetary A
Flywheel
Vacuum
Flywheel
Fracture
Lockup
Free Wheeling
Lockup
Loss of Pump
Breakup
Bearing Seizure
Sheared Shaft or
Loss of Gear Teeth
Bearing Seizure
Tri-hub
Rapid increase in engine
speed and vehicle speed.
Blow relief valve.
Loss of flywheel power,
High torque to transmis-
sion housing and mounting.
Overheating
Lockup or free wheel
Planetary A.
Shear joint or override
mechanism.
Bearing outer race slip,
Shear section.
Warning system.
Containment^
*Pathological failures.
-------
2. Freezeup of Element Three in the Secondary Hydrostatic Transmission
Again, this can result in a sudden unexpected change in vehicle speed
without driver command. Because the flywheel is tied to the engine, a
second effect could be flywheel overspeed.
3. Lockup of Planetary A.
Once again, the major effect will be the change in vehicle velocity with-
out driver command.
In all probability, pressure buildup, relief valve venting, and slipping of
the clutch and brake system will minimize this effect for all three of the
above faults. With respect to the planetary gearing, some form of shear joint
or override member could be introduced into the design to minimize or eliminate
this condition. Certainly the failure mode which could result in flywheel
overspeed would ultimately rely on some form of containment or possibly a
growthring-type of failure brake mechanism.
Control System
Regardless of the detailed source, a.failure in a control system signal com-
ponent becomes important only in terms of how it ultimately affects functioning
of the transmission and the flow of system power. For example, a variety of
detailed failures can occur in the components which control the secondary
transmission. The net result will be a value of the command transmission
ratio, either higher or lower than the correct value, which would result in
undesired vehicle deceleration or acceleration,respectively.
Viewed in this manner, failures in the control system can be analyzed as com-
mand errors in: 1) Primary Transmission Ratio, 2) Primary Transmission Range,
3) Secondary Transmission Ratio, 4) Mode Switching, 5) Engage-Disengage, and
6) Engine Throttle Position.
F-5
-------
Of these failures, the Primary Transmission Ratio, Primary Range, Secondary
Transmission Ratio, Failure of Mode Switching from Charge to Drive fall into
the pathological category as defined for the transmission. These, as well
as the loss of performance variety, are discussed below.
1. Primary Transmission Ratio
Errors in primary ratio result in improper loading at the engine shaft.
If a higher ratio is commanded, the vehicle will try to speed up the
engine shaft; a lower ratio will try to drag the shaft speed down.
Since the significant flywheel inertia will tend to hold the engine
speed constant, a step increase in primary ratio will also tend to
decelerate the vehicle as it accelerates the engine and flywheel. A
step decrease in primary ratio will tend to accelerate the vehicle.
Both deceleration and acceleration levels will be limited by the relief
valves in the hydrostatic links, but a step primary ratio error can re-
sult in a harsher and potentially more dangerous undesired velocity
change with a flywheel system than with a conventional vehicle where in-
ertia storage is much less.
2. Primary RanKfc
Results of errors in commands to the high-speed clutch and low-speed
brake are similar to malfunctions in those components as discussed
previously.
3. Secondary Transmission Ratio
Erroneous ratio commands to the secondary transmission will result in
undesired vehicle acceleration or deceleration due to flywheel action.
Although not exactly like a full pedal or brake input, a fast full sec-
ondary ratio error would call for essentially maximum acceleration or
deceleration capability of the flywheel augmented system.
F-6
-------
A. Mode Switching
As in a conventional vehicle, failures in tirade selection or establish-
ment logic mainly result in abnormal driving conditions with improper
available power or engine loading conditions. In a flywheel vehicle a
failure into the charge mode disengages the primary transmission and
could initiate abnormal flywheel chargeup until limited by the flywheel
velocity limit. Change without a command from charge to drive could
cause a brief vehicle acceleration burst.
5. Engage-Disengage
Failures in the primary and secondary engage-disengage systems lead to
inconvenient but not dangerous maloperation. Erroneous disengage opens
the hydrostatic links and causes loss of drive or flywheel capabilities.
Erroneous engage can lead to stalling the engine or prevent a startup.
6. Engine Throttle Position
As with a conventional vehicle, an erroneous throttle "on" command leads
to runaway vehicle acceleration. The "normal" driver response is to
apply the brake and/or cut the ignition.
Summary
As indicated, failures of certain transmission elements and control failures
leading to primary and secondary transmission ratio errors can result in po-
tentially dangerous vehicle acceleration or deceleration due to the special
energy storage capability of the flywheel.
In the preceding discussion, it was assumed that these types of malfunctions
would require the same type of driver reaction as conventional vehicles re-
quire. The malfunctions noted above which fall into the pathological category
would not be immediately corrected by the normal reactions of the driver. For
example, under abnormal conditions the driver would lift his foot from the
accelerator and apply the brakes expecting to slow down. He would still note
F-7
-------
an increase in vehicle speed or no indication of deceleration for a period of
time. Similar comments apply to the condition where unexpected decelerations
take place.
Although not included in our considerations.it is very probable that, should
the flywheel hybrid propulsion system come Into common usage, certain correc-
tive action could be built in and integrated with what would normally be ex-
pected from the driver.
Runaway accelerations can be simply guarded against by providing a solenoid
input to the secondary disengage valve such that the normal response of turn-
ing off the ignition will also open the secondary link.
Corrective action to abnormal abrupt deceleration is not as simple, since the
normal response to a quick surprise braking would not be to cut the ignition.
An automatic means for protecting against such a situation would be to sense
the vehicle gross acceleration or deceleration levels and disengage the secon-
dary l.f the respect I. vi.- levels are not commensurate wttli tlu1 existing accelera-
tor or brake pedal positions.
F-8
-------
SECTION G
REGENERATIVE BRAKING
3)
n>
-------
G. REGENERATIVE BRAKING ANALYSIS
In reviewing the requirements for dynamic (regenerative) braking, it was impor-
tant to assess the feasibility of braking and to determine if the use of flywheel
dynamic braking would unduly penalize the overall transmission design. In the
latter case, this would require a trade-off between any added complexity or
design compromise and the extent of their benefit. In terms of assessing feasi-
bility, this was considered on the basis of a total energy concept, practical
braking limits for vehicles, peak torque and horsepower requirements, and any
other influences brought about by the flywheel.
In terms of the total energy concept, there is no real question that in theory,
sufficient energy can be absorbed in the flywheel to effectively absorb the
kinetic energy of the vehicle in going between two speeds. The questions have
to do with the practical limitations of road coefficient of adhesion, flow of
power from the rear wheels only, and possible modifications if some combination
of flywheel and mechanical braking is required for overall vehicle passenger
safety.
One of the primary considerations with respect to braking must concern itself
with operator or passenger safety. Therefore, the initial point for assessment
concerns itself with an emergency stop type situation, which for analysis pur-
2
poses was taken to be a deceleration rate of 20 ft/sec . For purposes of estab-
lishing the outside limit, a vehicle weight of 5300 Ibs. was selected and a
factor to compensate for the inertia of wheels and transmission parts of 1.05 was
applied to this value giving a total equivalent vehicle weight of 5565 Ibs. The
2
deceleration rate of 20 ft/sec is equivalent to a coefficient of road adhesion
of 0.62 which gives a braking force of 3450 Ibs. with the above vehicle weight.
During a deceleration of this magnitude, the distribution of vehicle weight is
such that approximately 35 percent will be applied to the rear wheels. This
represents a rear wheel braking force of 1208 Ibs. At this point, several
conclusions regarding the braking situation can be made:
1. For an emergency stop, braking must utilize an assist to the dynamic
G-l
-------
braking possible from the flywheel since only 35 percent can be
dissipated through the rear wheels.
2. There is a limitation with regard to regeneration if this is to
come purely from rear wheel braking energy alone. (The engine
must make up at least 65 percent of the total flywheel energy
required.)
3. Energy dissipated from other elements such as front wheel brakes
and the combined effects of air resistance and rolling resistance
are not recovered as regeneration energy.
There are several implications of the above data with respect to operator safety.
Certainly the basic conclusion is that there can be modes of operation where the
flywheel would be unable to dissipate the required energy necessary for emergency
stopping. Recent literature indicates that one-half g stops are certainly com-
2
mon and that the use of a 20 ft/sec stopping rate is not unreasonable. (See
Reference 7.) Thus, it is concluded that the four-wheel braking capability
currently utilized in vehicles could not be eliminated nor significantly com-
promised. However, further consideration must be given to other implications of
the system and lesser rates of deceleration which are more consistent with the
typical driving cycle. Before discussing these, it is appropriate to consider
some additional qualitative implications suggested by the above discussion.
These items are as follows:
1. If recuperation of the flywheel is achieved by dynamic braking and
engine input, there is a dual power path which involves additional
complexity in control. Extreme care would be necessary to pre-
clude the rotating inertia from coupling to the vehicle to reflect
itself as an even larger equivalent vehicle weight.
2. During this engine-assisted flywheel charging process, it would
be an additional control requirement to match the conditions
necessary to maintain a reasonable engine specific fuel consump-
tion.
G-2
-------
Based on the above it is logical to consider the lower rates of deceleration and
recovering energy as a retarder which might be set up with minimum modification
and provide added brake-shoe life on both front and rear wheels. In order to
demonstrate this we considered the same road coefficient of adhesion (0.62), an
effective vehicle weight of 5565 Ibs., and took into account the revised weight
distribution resulting from the deceleration rate to determine that a decelera-
2
tion of 8.2 ft/sec would just permit regeneration. The braking force corres-
ponding to this rate of deceleration is 1,417 Ibs. As in the previous calcula-
tions, the effects of air resistance and rolling resistance were neglected since
this is a conservative approach with respect to braking safety. Figure G-l shows
the braking behavior for the maximum tractive force and constant rates of decel-
eration.
2
Since the deceleration of 8.2 ft/sec was determined to be the value where full
regeneration was possible, this was considered further in terms of the transmis-
sion system concept. One of the important factors concerning the ability of the
system to provide recuperation is the instantaneous flow of power which must be
delivered from the rear wheels to the flywheel. At 85 miles per hour, the in-
stantaneous power requirement is 319.7 lip. The size of the hydrostatic compo-
nents permits a peak power transfer rate of 164.4 hp. This power is referenced
to the wheels and includes the braking benefits due to system losses. In terms
of a rear wheel braking force, the 164.4 hp corresponds to 725.6 Ibs. The con-
clusion here is that to achieve regeneration up to a maximum deceleration rate
2
of 8.2 ft/sec , the capacity of the flywheel transmission must be doubled. The
attached Figure G-2 shows how the system could be altered to realize this addi-
tional capacity. The added components and control complexity were estimated to
add between 12 and 15 percent to the overall transmission cost.
Finally, the flywheel was considered for a retarder. In essence this considered
that the maximum braking force available would be the 725.6 Ibs. If this is now
used in conjunction with normal brakes for an emergency deceleration, again
2
taken to be 20 ft/sec , the flywheel would be capable of absorbing approximately
16.8 percent of the vehicle kinetic energy when stopping from 85 miles per hour.
The above calculation is based on an assumption of 80 percent efficiency in
returning the regenerative energy to the flywheel. Still another way to consider
this is to determine what deceleration or retarding capability could be provided
G-3
-------
.3 x 10 KE Flywheel at 10,000 RPM
Max. KE of Vehicle (1.4 x IO6)
10
5 ft/sec
v
f
7
1.7 x IO6 KE Flywheel
at 24,000 RPM
o
.—i
x
1
4J
14-1
t>0
Cd
0)
AKE
Required
of
Flywheel
.3 x 10 KE Flywheel
at 10,000 RPM
io
Braking KE - .62 Coefficient
Decel. = 10 ft/sec2
Braking KE Available at Rear Wheels
.62 Road Coefficient
Decel. = 20 ft/sec2
Brake KE Matches Vehicle KE
When: Decel. = 8.17 ft/sec2,
Road Coefficient = .62
i i
l l l i i
20 30 40 50 60 70 80 10 12 14 16 18 20 24
MPH
Flywheel RPM x 10
o
Fig. G-l Flywheel Regenerative Braking Behavior
G-4
KII-12502
-------
O
Ul
Bngin_£
Input
\e
J
1
]
J
r~
r
~
F—
t L _-
1
]
P
I
b
~
s
1
1
^
\T)
T C • 3
7 . 5 in
FD
7.5 in3
VD
7.5 In3
J
FD
3
7 .5 In
VD
7.5 in3
F
i
i
4
Output
to Rear
Axle
Fig. G-2 Power-Splitting Transmission Sized for Regenerative Braking
MTI-12503
-------
by the flywheel transmission as shown in Figure B-l, page 9-2'-. In this instance,
the flywheel i
regeneration.
2
the flywheel could provide a deceleration capability of 4.41 ft/sec with full
It was felt that the above represented reasonable guidelines for what could be
expected from regenerative braking. There are obviously certain technical
problems which would have to be resolved to take advantage of the flywheel even
as a retarder. For example, there would have to be some mechanism provided so
that the proper braking force at the rear wheels could be shared by the rear
wheel brakes and the flywheel circuit in agreement with the proportion discussed
above. This would, in turn, have to be reconsidered in terms of the implication
on safety. Automatic retarding action would be realized when there was no
throttle requirement (foot removed from the accelerator).
G-6
-------
H. REFERENCES
1. Environmental Protection Agency, Advanced Automotive Power Systems,
"Vehicle Design Goals - Six Passenger Automobile," Revision C,
May 28, 1971.
2. Lockheed Missiles and Space Company, "Flywheel Feasibility Study and
Demonstration," Final Report LMSC-D007915, April 30, 1971.
3. Automotive-Industries, March, 1969, Page 131.
4. Lockheed Missiles and Space Company, Letter LMSC-D179983
0/50-33, B/528, August 12, 1971.
5. Lockheed Missiles and Space Company, Letter LMSC-D244218,
October 20, 1971.
6. David N. Hwang, "Fundamental Parameters of Vehicle Fuel Economy and
Acceleration," Paper //690541, Society of Automotive Engineers,
October 30, 1968.
7. Rudolf G. Mortimer, "Hard Braking is More Common Than You Might Think,"
Automotive Engineering, August, 1971.
H-l
-------
TJ
m
Z
g
x
-------
APPENDIX I
DESCRIPTION OF METHODS FOR
DETERMINING TRANSMISSION AND PROPULSION SYSTEM PERFORMANCE
Presented herein are (1) a discussion of the transmission performance analysis,
(2) a description of the computer program for steady-state performance, and (3)
a discussion of the digital dynamic simulation used for determining transient
performance.
A. Transmission Performance Analysis
The transmission is considered to comprise the following components:
• Spur Gears
• Planetary Gears
• Pumps
• Motors
In transmitting power either under steady or transient conditions, each of these
components is a source of power loss. The losses considered may be grouped into
three types:
1. Mechanical Losses
Mechanical losses always act to oppose rotation of a shaft, and arise
from such sources as friction in the bearings, friction at gear teeth,
and windage. All of the components listed above are subject to
mechanical losses.
2 . Flow Losses
Flow losses represent deviations from ideal performance of a hydraulic
pump or motor. Thus, while nominal performance assumes that pump flow
T
(in /sec) is equal to the product of speed (rad/sec) and displacement
(in /rad), the actual flow differs from this product by a small amount
— similarly for the motor. The direction in which flow losses act is
determined by the direction of power flow. Only hydraulic units are
subject to flow losses.
1-1
-------
3. Compressibility and Leakage Losses
Compressibility and leakage losses represent deviations from ideal
performance in the transfer of flow from one hydraulic unit to the
other. Thus, while nominally the flow transferred to the motor equals
the flow generated by the pump, the actual or effective flows differ
by a small amount due to compressibility of the fluid and leakage
through seals. The direction in which compressibility and leakage
losses act is also determined by the direction of power flow.
Only the hydraulic units are subject to compressibility and leakage
losses .
The treatment of the various components including losses is as follows:
Spur Gears
Wheel 1
Wheel 2
Speed Equation:
Mechanical Loss Equation:
Normal Direction of Power Flow
(I-D
(1-2)
where
R is the gear ratio
T , T are the input and output torques acting in the normal direction
of rotation
NI, N- are the input and output speed
1-2
-------
T) is the efficiency of transmission
I (1 — T])T1 represents the absolute value of the quality (1 — Tj)T1
Sign (N ) represents the algebraic sign of the quality N ; i.e.,
if N is positive, Sign (N..) = +1; if N^ is negative,
Sign (N) = -1.
Planetary Gears
V \
Cage
T N
'
Assumed Normal
Direction of
Power Flow
Speed Equation:
N,. = N.
•S *R
Mechanical Loss Equations
(1-3)
T = T - T
S S LS
= T — T
R LR
(1-4)
T = T + T
C C LC
Torque Relationships:
(1-5)
Ts'
1-3
-------
Mechanical Loss Definition:
LS
LR
-------
Flow Loss Equation:
Qp - NpDp
Pressure Calculation:
P = Tp'/Dp
sign (NpTp))
(1-6)
(1-7)
Motors
P»QM
Normal Power Flow Direction
Mechanical Loss Equation:
T = T — T
M M LM
where
LM
P TT-
max
Flow Loss Equation:
(K2M + K3M °P
sign (NM)
(1-8)
(1-9)
Transfer of Flow From Pump to Motor
QM = QP ~ Q
where
LC
QLC = LlP/Pmax
K1L + K2L + K3L
+ [KIL] | QM
(1-10)
In calculating hydraulic transmission performance, the pump and motor are
considered in combination. Equations (1-5) through (1-9) relate the six
values of torque, speed and displacement for the pump and motor in such a
1-5
-------
way that given four of the six values, the remaining unknown two may
be determined.
In the above treatment of hydraulic units, the following definitions apply:
T ,31 are the input torque to pump, and output torque from the
motor respectively.
Dt>»Dv< are the pump and motor displacements
r el
D is the ratio of pump displacement to its maximum value
for the unit
N ,N are pump and motor speeds, rad/sec
Nn>N.. are ratios of pump and motor speeds to the maximum
f M
values for the unit
2
P is pressure, Ib/in
P is maximum pressure value for the unit
max
K is a flow loss coefficient (see below for values imposed
...^,
In 3M
for all loss coefficients)
are mechanical loss coefficient
,K ,K are coefficients relating to compressibility and leakage
1L 2L JL
n>«
P M
losses
o
are tne effective pump and motor flows, in /sec
Q is a leakage flow
LC
Additional Losses
In addition to losses in gears and hydraulic units, further losses are con-
sidered to occur at various points in the transmission to account for the
power needed to drive such components as the flywheel vacuum pump. (See
Figures AI-1 and AI-2 — Parasitic Losses.) Such losses are treated in
a manner exactly analogous to the spur gear losses using a unit gear ratio.
Additional losses are also considered to overcome flywheel windage and
bearing friction (as specified by LMSC), to overcome road resistance (as
specified by EPA).
1-6
-------
PRIMARY HYDRAULICS
TpL=0.985
Actuator
Stroke
Tl = 0.99
Te,N
e.e
Parasitic
Losses
T| =1.00
Secondary Planetary
Element
Element
II
SECONDARY HYDRAULICS
R = Gear Ratio
r = Gear Radius
Ne = Engine Speed
0.96
I^U.b
rR
rs
V
»J
1
l| -u. -y
R6
1
?
N3
Element
III
Element
IV
N4
"; = U.VB.
R5
Actuator
Stroke
Fig. AI-1 Power-Splitting Transmission - Low-Speed Range Diagram
Wh e e1s
HTI-12516
-------
i
oo
Actuator
Stroke
PRIMARY HYDRAULICS
1) = 0.99
I T — _r\ nn
odge
NFI
I T| = 0.99
SECONDARY HYDRAULICS
Sun
i sun i
SECONDARY PLANETARY
rR
rs
N6 "
" 1
1
D
R6
Ring 1
N3
Element
III
Element
IV
\
T]=0.985
R5
PRIMARY PLANETAR"
Actuator
Stroke
R = Gear Ratio
r = Gear Radius
N'e = Engine Speed
Fig. AI-2 Power-Splitting Transmission — High-Speed Range Diagram
MTI-12548
-------
Numerical Values for Efficiencies and Loss Coefficients
The loss coefficients and mechanical efficiency numbers for the considered
components were generated from previous experimental work.
Values for mechanical losses were typical for the type of gearing specified
in the transmission design. The numerical values of efficiency used for
performance calculations are shown in Figures AI-1 and AI-2 for the low-
speed and high-speed ranges, respectively. The loss associated with TL
has a minimum value of 1.5 hp at engine speeds above 3200 rpm. At lower
speeds the minimum loss is linearly interpolated between 1 hp at 1400 rpm
and 1.5 hp at 3200 rpm.
The equations defining losses in all hydraulic elements (presented earlier)
were correlated to experimental data obtained for similar hydraulic units
operating in various different transmissions that ranged in power rating
from 25 to 200 horsepower. The resultant values of hydraulic element loss
coefficients employed in all performance analysis calculations were as
follows:
K = 0.0225 K = 0.0075
1 r 1L
^M = °'°25 K2L = 0>°25
*™ = °-005 KQT = 0.005
jM JL
B. Digital Computer Program for Steady-State Performance Analysis
In broad terms, the computer program operates by moving backwards, from the
wheels and the flywheel, towards the engine. At each point in the transmission
the program calculates the torque required to overcome all hydraulic and mechan-
ical losses between that point and the wheels or flywheel, together with the
torque to overcome resistance to motion of the wheels (resistance specified by
EPA) or flywheel (windage and friction specified by LMSC). The flywheel speed
is related to the wheel speed by the TKE relationship. The primary and secon-
dary (flywheel) transmissions are linked together to satisfy the necessary speed
and torque relationships of a geared torsional system under steady-state operation.
1-9
-------
The above statement of operation requires the addition of some constraint to
define engine speed. The standard procedure followed by the program is to seek
the engine speed which provides the necessary power at a condition of minimum
SFC. To do this and not overconstrain the problem it is necessary to leave one
displacement in each of the two hydraulic power converters undefined. The
program then establishes the displacement value for each hydraulic power con-
verter which provides the necessary transfer of speed and torque. Thus, in
addition to calculating performance, the program provides a means of defining
the primary and secondary displacement schedules as a function of speed.
Under certain conditions of speed and load, steady-state operation on the minimum
SFC line cannot be achieved, due to displacement limits of the hydraulic units or
limits on the engine speed. These special conditions will be amplified subse-
quently .
Detailed Program Procedure
The following sequence of operations describes the actual procedures followed by
the computer program. Figures AI-landAI-2 provide a reference for this descrip-
tion. The terms upstream and downstream describe relative locations which,
respectively, follow or oppose the arrows of Figures AI-1 and AI-2 . Operation of
the transmission in low range (Fig. AI-1) is described first (items 1-20) followed
by modifications (items 21-25) to handle the high-range operation (Fig. AI-2)
1. For each vehicle speed of interest the program initially calculates
the resistance torque to be overcome at the wheels, which must, there-
fore be supplied to the wheels by the transmission. This torque is
based on EPA specifications.
2. The flywheel speed corresponding to the vehicle speed of interest is
calculated via the TKE relationship.
3. The flywheel windage and friction losses corresponding to this flywheel
speed are calculated according to LMSC specifications.
4. That engine speed is calculated which will provide the required power
at minimum SFC. This first calculation of speed is made assuming no
intermediate losses apart from resistance and windage.
1-10
-------
5. Using equations 1-1 and 1-2, the speed and torque acting immediately up--
stream of the rear .axiel %. differential (RA) are computed.
6. Using equations 1-1 and 1-2, the speed and torque acting immediately up-
stream of the output gear ratio (R3) are computed.
7. Using equations 1-1 and 1-2, the speed and torque acting immediately up-
stream of the primary hydraulic output gear (R2) are computed.
8. Using equation 1-1, the speed downstream of the primary pump input gear
(Rl) is calculated from the current value of engine speed.
9. Using equations 1-6, 7, 8, 9 and 10, with pump and motor speed, motor
torque, and motor displacement specified, the pump displacement and pump
torque are determined for the primary hydraulic power converter (this
system of equations is mildyly non-linear in displacement, but is solved
effectively by direct (Picard) iteration).
10. Using equation 1-2, the torque upstream of the primary pump input gear
(Rl) is calculated from the torque at input to the primary pump
(element I).
11. Using equations 1-4 and 1-5, the torques at the ring and cage of the fly-
wheel planetary are calculated from the flywheel windage torque (sun
torque).
12. Using equation 1-3, the speed of the ring of the flywheel planetary is
calculated from the flywheel (sun) and engine (cage) speeds.
13. Using equation 1-2 for R,, the torque acting at output from the secondary
motor (element III) is calculated.
1A. Using equation 1-1 for R ,_the speed of the secondary pump (element IV)
is calculated from the engine speed.
15. Using equations 1-6, 7, 8, 9 and 10 with motor torque, motor speed, motor
displacement and pump speed specified, the pump torque and displacement
are calculated for the secondary hydraulic power converter. (Direct
iteration is again used to handle the non-linearities in this system
of equations).
16. Using equation 1-2 the torque upstream of the secondary pump gear (R,) is
calculated.
17. All the torques acting on the engine output shaft downstream of the
parasitic losses are now defined. These torques are added to give the
torque downstream of the parasitic losses.
1-11
-------
18. Equation 1-2 with a gear ratio uf unity is imposed to calculate the
power upstream of the parasitic losses, which is also the engine output
torque.
19. From the engine performance charts the engine speed to define this
torque at minimum SFC is interpolated.
20. The above procedure, starting at item 5, is repeated until engine speed
and displacement values are repeatable between successive iterations
within 1 part in 10,000.
For operation of the transmission in the high range, the following steps replace
Steps 6 and 7:
21. Using equation 1-1 for gears R and R ~, the speed downstream of R n
is calculated. This speed is also the cage speed for the output
planetary.
22. With cage and ring (upstream of R.) speeds specified, equation 1-3 is
used to calculate the sun speed - which is the speed downstream of R .
23. Using equation 1-4 and 1-5, the sun and cage torques for the output
planetary are calculated. The sun torque is the torque downstream of
R . The cage torque is the torque downstream of R-.
24. Using equation 1-2 for ratio R,n, the torque upstream of R n is cal-
culated from the cage torque.
25. Using equation 1-2 for ratio R , the torque upstream of R is cal-
culated.
Apart from the above modifications to handle the output planetary and ratios
Rq and R-,n» the treatment for high-range operation parallels that for low-
range operation.
The following additional constraints apply:
A. If the speed which provides the required torque at minimum SFC is less than
1400 RPM or greater than 3800 RPM, the desired speed is taken to be 1400 RPM
or 3800 RPM respectively.
1-12
-------
B. If any of the engine speed requirements call for displacements of either
of the primary hydraulic units which exceed the allowable limits, then the
value of displacement is set at that limiting value and the equations
solved for engine speed. This constraint override!* Constraint A.
Sample Calculation
Table AI-1 shows sets of computed quantities at vehicle speeds of 20 and 70 MPH.
The tables include quantities at every major point in the transmission.
C. DIGITAL DYNAMIC SIMULATION ANALYSIS AND COMPUTER PROGRAM
For the purposes of dynamic analysis the vehicle and transmission are modeled
as a three-inertia system consisting of the Engine (J ), Flywheel (Jf), and
Output (J ) inertias. The output inertia represents the vehicle mass referred
o
to the rear axle. All secondary inertias are referred to the appropriate speed
and combined with one of these three model inertias.
The equations of motion for the three inertias are:
J N = T - T (1-11)
o w w R
J N = T. - T (1-12)
e e me ^
JfNf
Where N , N , Nf are the angular speeds of the output, engine, and flywheel
inertias respectively in rad/sec.
T is the torque transmitted to the wheels via the transmission
T is the resistance torque acting on the wheels (rolling, wind and
grade as specified by EPA)
1-13
-------
TABLE AI-1 TYPICAL DETAILED RESULTS OF STEADY-STATE
PERFORMANCE COMPUTER PROGRAM
INPUT DATA:
Vehicle Weight
Cd x A
Grade
Ambient Temperature
Ambient Pressure
Fuel Density
4600 LB
12.00 FT2
0.00 Per Cent
85.00 °F
14.70 PSI
6.152 LB/CAL
Gear ratios as specified In Fig. B-l
Engine characteristics as specified by EPA
Pierced Flywheel - chamber pressure = 2.94 PSI
Resistance losses as specified by EPA
VEHICLE VELOCITY
Power Train Efficiency
Transmission Efficiency
Primary Efficiency
Secondary Efficiency
Wheel Speed
Output Speed
Flywheel Speed
Engine Speed
Speed At Element I
Speed At Element II
Speed At Element III
Speed At Element IV
Road Torque
Output Torque
Flywheel Torque
Engine Torque
Torque At Element I
Torque At Element II
Torque At Element III
Torque At Element IV
Road Horse Power
Output Horae Power
Flywheel Horse Power
Engine Horse Power
HP At Element I
HP At Element II
HP At Element III
HP At Element IV
Auxiliary Horse Power
Fuel Flow
SFC
MPO
Displacement Of Element I
Displacement Of Element II
Displacement Of Element III
Displacement Of Element IV
Primary Pressure
Secondary Pressure
Ideal Flow At Element I
Ideal Flow At Element II
Ideal Flow At Element III
Ideal Flow At Element IV
Effective Flow At Element I
Effective Flow At Element II
Effective Flow At Element III
Effective Flow At Element IV
Primary Leakage Flow
Secondary Leakage Flow
20 M.P.H.
70 M.P.H.
37.114
87.100
100.317*
97.135
266.774
947.049
23444.553
1400.000
1102.360
142.699
-1991.470
1272.740
90.400
26.483
-1.344
74.974
-1.549
-12.003
-9.003
14.502
4.592
4.775
-6.001
19.985
-0.325
-0.326
3.414
3.514
7.613
12.276
0.614
10.023
0.968
7.500
3.633
-5.841
120.661
187.056
17.788
17.837
-120.584
-123.901
17.806
17.835
-122.723
-123.070
-0.029
-0.347
per cent
per cent
per cent
per cent
RPM
RPM
RPM
RPM
RPM
RPM
RPM
RPM
Ft. Lb.
Ft. Lb.
Ft. Lb.
Ft. Lb.
Ft. Lb.
Ft. Lb.
Ft. Lb.
Ft. Lb.
HP
HP
HP
HP
HP
HP
HP
HP
HP
Lb. Hr.
Lb. Hr. HP
In3/Rev
In-j/Rev
In /Rev
In /Rev
Psi
Psi
In^/Sec
In,/Sec
In^/Sec
In /Sec
In^/Sec
In,/Sec
In^/Sec
In /Sec
In^/Sec
In /Sec
82.864
90.355
95.172
100.886*
933.710
3314.671
15911.520
2817.460
2218.468
-2835.430
802.989
2561.353
244.733
71.696
-0.724
125.222
45.419
-33.821
-4.657
-1.447
43.508
45.248
-2.193
67. 174
19.185
18.259
-0.712
-0.706
14.669
35.309
0.526
12.196
-7.500
5.625
5.500
1.710
455.166
63.831
-277.308
-205.822
73.607
73.004
-272.983
-271.121
73.413
73.192
-1.862
-0.221
per cent
per cent
per cent
per cent
RPM
RPM
RPM
RPM
RPM
RPM
RPM
RPM
Ft. Lb.
Ft. Lb.
Ft. Lb.
Ft. Lb.
Ft. Lb.
Ft. Lb.
Ft. Lb.
Ft. Ub.
HP
HP
HP
HP
HP
HP
HP
HP
HP
Lb. Hr.
Lb. Hr. HP
Inil/Rev
In^/Rev
In,/Rev
In /Rev
Psi
Psi
In^/Sec
In^/Sec
In^/Sec
In /Sec
In^/Sec
In^/Sec
In^/Sec
In /Sec
In^/Sec
In /Sec
Efficiency > 1007. Implies that flow of power is in reverse of arrows in Figs. Al-1 and
AI-2 (see values for power).
1-14
MTl-12335
-------
T is the engine input torque
in
T is the engine output torque (acting on transmission)
e
T . , is the windage and friction torque acting on the flywheel (as specified
wind
by Lockheed)
T is the flywheel output torque (acting on transmission)
The interrelationship between the system torques, including mechanical losses
follows the treatment of Section A of this Appendix.
The flow, compressibility and leakage losses are also calculated according
to the procedure of Section A of this Appendix.
Thus, the torques T , T_, T. , T , T . ,, T,, can be calculated at any time, t,
w K in e wind t
as a function of the three velocities N , N N , and the primary and secondary
w i e
pressures.
In determining the pressure in the hydraulic units the treatment differs from
the steady state procedure. Under dynamic conditions, the rate of change of
pressure, rather than the pressure itself is determined by the torques and
speeds of the pump and motor as follows:
= (1-14)
at v v '
where: p is the pressure
6 is the bulk modulus of the fluid
Q is the net mismatch in pump and motor flows
V is the volume of fluid in the unit.
/t-15
-------
Equation 1-14 is applied both to the primary and to the secondary hydraulic
transmission units. Thus, together with the three equations of motion, 1-11,
12, 13, the dynamics of the mechanical and hydraulic system are described by
5 dynamic equations, and the torque-speed pressure relationships of Section A
of this Appendix. A further series of dynamic equations define the performance
of the control system, whose function is to adjust the displacements of the
hydraulic units in response to commands of the pedal and requirements of main-
taining constant IKE. The control system is defined by the full range block
diagram, Figure AII-7.
The complete system of twelve equations defining the dynamic performance of the
vehicle and transmission in response to pedal commands is solved via a fourth
order Runge-Kutta integration algorithm. Output quantities are printed at
regularly spaced time intervals (typically every 0.1 sec).
The following quantities are calculated and printed by the computer program as
a function of time.
Vehicle Velocity
Vehicle Acceleration
Wheel Speed
Flywheel Speed
Engine Speed
Transmission Output Speed
Wheel Torque
Road Torque
Engine Input Torque
Engine Output Torque
Flywheel Loss Torque
Flywheel Output Torque
Transmission Output Torque
Engine HP
Road HP
Flywheel HP
Overall Efficiency
Overall Transmission Efficiency
Primary Efficiency
Secondary Efficiency
Fuel Flow
Specific Fuel Consumption
MPG
Speed, Torque, HP at Hydraulic Units
1-16
-------
Primary Pressure
Secondary Pressure
Displacements of Hydraulic Units
Ideal Hydraulic Flows
Cumulative Fuel Consumption
Cumulative Engine HP-Sec.
Cumulative Flywheel HP-Sec.
Input to the computer program consists of:
Initial Values of Spped, Pressure, Control Settings
Control Gains, Time Constants
Hydraulic Fluid Compressibility
Primary, Secondary Volumes
TKE
Wheel Radius
Grade
Car Frontal Area
Wind Resistance Coefficient
Ambient Pressure, Temperature
Vehicle Weight
Accessory HP Tables as a Function of Engine Speed
Engine Performance Tables
Idle Fuel Flow
Inertia Values
Gear Ratios
Sun, Gear, Cage Radii for Flywheel and Output Planetary Gears
Mechanical Efficiencies
Compressibility, Leakage and Flow Coefficients
Numerical Integration Controls
Range Switch Controls
Limits of: Pressure; Fuel Flow Rate of Change; Actuator Position;
Displacements; Rate of Change of Actuator Position.
1-17
-------
APPENDIX II
STABILITY AND ANALOG COMPUTER SIMULATION ANALYSIS
Presented herein is a discussion of the stability analysis performed for the
transmission as an integral part of the flywheel/hybrid propulsion system. This
is followed by a discussion of the related analog computer simulation analysis.
1. Stability Analysis
The objectives of the linearized stability analysis were:
A. To determine whether the feedback control loops are basically
stable or unstable.
B. If unstable loops exist, add compensation as required to obtain
stable operation.
C. To determine the optimum (maximum allowed) gain values. If the
gains are too low, the transient response will be too slow. If
the gains are too high, the system will be unstable.
From a general viewpoint, open loop gain and phase lag both vary with frequency.
If the phase lag between the input to a control loop and the feedback signal is
180 degrees and the gain is 1.0 (zero decibels) or greater at the same frequency,
the loop will be unstable. The open loop gain is usually set to give zero
decibels at about 135 degrees, to provide adequate damping.
Stability analysis techniques apply only to linear systems. Therefore, the sys-
tem nonlinearities must be replaced with equivalent linear functions. The gain
varies with the operating point for a nonlinear system. Therefore, stability
must be investigated over the full range of the parameters.
The effects of nonlinearities and interaction between control loops is best
investigated on an analog computer. Some modification of the calculated gain
values is usually required because of these effects.
II-l
-------
The full-range nonlinear block diagram for the complete system is shown in Figure
AII-7. The linearized block diagram of the secondary control system is shown in
Figure AII-1. The linearized models were derived from the nonlinear block diagram.
Secondary Transmission Control
The secondary transmission has two integrations: one from the flywheel, and one
from the piston actuator. Since two integrations provide 180 degrees phase lag
at all frequencies, the secondary transmission will be unstable for any reasonable
gain unless feedback compensation is used to reduce the phase lag. Two types of
feedback around the piston actuator were considered: a mechanical feedback
linkage and pressure feedback.
The steady-state displacement of hydrostatic Element IV, D,,* varies with the
values of engine speed and flywheel speed. With a mechanical feedback linkage
around the secondary piston actuator, D, is given by
K13 K4
D4 - -if— AKE
where:
Kf = feedback gain around primary piston actuator
AKE = kinetic energy error
Thus, a kinetic energy error is required to maintain a steady-state value of D .
The kinetic energy error is proportional to D,. The kinetic energy error inher-
ent with this type of feedback would not be desirable.
With pressure feedback, a kinetic energy error is not required to maintain
steady-state values of D,. The pressure feedback is equivalent to flywheel
torque. Thus, with pressure feedback, flywheel torque is proportional to kinetic
energy error. At steady-state, the kinetic energy error is proportional to fly-
wheel friction. Flywheel friction torque is small compared to the maximum fly-
wheel torque. Therefore, the steady-state kinetic energy error will be small.
*Nomenclature is given at the end of this Appendix.
11-2
-------
At a constant value of D,, an increase of engine speed results in an increase of
flywheel speed. Engine speed is an undesired signal input to the secondary con-
trol system. Pressure feedback will reduce the effect of this undesired engine
speed input. Pressure feedback will also reduce any tendency of the secondary
transmission pressures to saturate. Therefore, pressure feedback was selected
to reduce the phase lag of the piston actuator.
The linearized block diagram of the secondary control system is shown in Figure
AII-1. The speed of hydrostatic Element IV, N, , is considered constant in the
linearized model. The square function in the flywheel speed feedback was
linearized as follows. The square function is described by the equation
Nf2 (II-l)
Differentiating
AX = 2 N ANf (H-2)
In Equation II-2, ANf and AX are the linearized variables. 2Nf is the gain of
the square function. Next, the open-loop gain and phase lag versus frequency
curves were plotted (Bode plots). A Nichols chart was used to determine closed-
loop frequency response from the open loop Bode plot.
Figure AII-2 shows open- and closed-loop Bode plots of the inner control loop with
pressure feedback, K . The gain of this loop varies with engine speed by 2.7
(9 db) over the operating range. The gains must be selected for adequate damping
at the highest engine speed. The highest open-loop gain for stable operation at
3800 rpm engine speed is 18 (25 db) as shown in Figure AII-2. The required com-
bined value for the gain parameters K and K, for 25 db open-loop gain is K K, =
4.1 x 10~5.
Figure AII-3shows the Bode plots for the secondary transmission outer loop with
linearized flywheel speed feedback. The maximum allowable gain at maximum engine
speed and maximum flywheel speed is 8.5 (18.5 db). The required value of the
II-3
-------
*»
1/L2
TPS
Nf ^
Fig. AII-1 Linear Block Diagram — Secondary Control System
MTI-12545
-------
-20
Frequency, (Rad/Sec)
100
Fig. All-2 Bode Plots - Secondary Transmission Inner Loop
MTl-12339
-------
20
Open Loop Cain at
Ne - 3800 RPM
Nf - 24, .000 RPM
Closed Loop FH«se Lag at
3800 RPM
24,000 RFM
Ne - 3800 RPM
200
ISO
7\
Closed Loop Gala it
- 3800 RFM
\Ne - 380
Nf - 2*.
000 RPM
100
-20
\\
X
50
Closed Loop Gain at
- 1400 RPM
- 10.000 RPM
\
Closed Loop Gain at
Ne - 1400 RPM
Nf - 24.000 RPM
10
Rod/Sec
100
Fig. AII-3 Bode Plots - Secondary Transmission Outer Loop
MTI-12337
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gain parameters K and K to give 18.5 db outer loop gain is K /K = 0.264.
Primary Control System — High Range
The linearized block diagram for the primary control system in high range is
shown in Figure AII-4- This block diagram includes the engine and vehicle
dynamics. It is necessary to simplify this model before applying linear analysis
techniques due to the number of feedback loops.
There are two parallel feedback paths from P.. (the hydrostatic differential
pressure) to the gain block R2 D_. The gain through the vehicle is less than
the gain through the engine by a factor of about 100. Therefore, the signal
path through the vehicle has negligible effect on primary control stability,
and this path can be eliminated from the model. The signal through gain block
RI P./12 is small for normal values of P.. ; therefore, this path can also be
omitted from the analysis.
There are two feedback loops from engine speed, N , to the compressibility block.
Closing these loops gives the transfer function
N
e
2c s + _i^ S2
(0 io/2
n n
The parameters of the transfer function vary with the value of D.. as shown below
in /rad
0
+1.19
-1.19
C
0.52
0.35
1.03
Ll
rad/sec
158
80
80
C
0.085
0.17
0.17
The set of parameters having the greatest effect on stability is on the lower
line since the gain is highest and the natural frequency is lowest. Those
parameters were used for the inner loop transfer function. The open- and closed-
loop Bode plots for the outer loop are shown, in Figure AII-5. The inner-loop
dynamics actually have negligible effect on the outer loop dynamics. The value
II-7
-------
i
oo
R1D1
Actua tor
Compressibility
Engine
+ 1 -
ec
K,
+ f +
1/Ll
l+TpS
R2D2
*2R12D2
12 12
Ripio
12
m
R12
RaR10
Vehicle
11 2
12
11
+1
Fig. AII-4. Linear Block Diagram - Primary Control System - High Range
-------
30
20
10
.o
•H
u
01
O
-10
-20
'Open Loop Gain
Open Loop Phase Lag
Closed Loop Gain
10
Frequency, (Rad/Sec)
200
60
«
01
00
4
03
(II
4)
M
00
100
100
Fig. AII-5. Primary Control System Frequency Response
IT-9
-------
of gain term K. which was used for this ^ode plot is K_ = 3.68 x 10
Primary Control System — Low Range
The linear block diagram for the primary control system in low range is shown in
Figure AII-6. The signal paths through the vehicle inertia and R. P,/12 gain
block can be omitted for reasons explained in the high-range analysis. Closure
of the inner feedback loop gives the transfer function
N C0
e 2
_ +
0 2
n2 »
where
C2 - 1.35
C2 = 0.25
u) „ = 52 rad/sec
n/
The outer loop is not closed over most of the low range since Hydrostatic Element
I, Displacement D , does not change. At the upper end of the low range, the
outer loop is closed. The outer loop is then the same as in the high range. The
primary control system is therefore stable in low range. At the upper end of the
low range, damping is a little lower than in the high range due to the higher
gain, and lower natural frequency of the inner loop.
Results of Stability Analysis
The stability analysis above thus indicates that both the primary and secondary
control systems are basically stable with the gain values established.
2. Analog Computer Simulation
The objectives of the analog computer study were to:
A. Verify validity and accuracy of mathematical model.
B. Modify the gain values determined from the linear analysis, if required,
to compensate for the effect of nonlinearities.
11-10
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'ec
RLD1
Actuator
dl
+ 1'-
1/L1
1-t-T S
R1D1
12
R1P10
12
J0S
Vehicle
Engine
5N/oT
Fig. AII-6. Linear Block Diagram - Primary Control System - Low Range
-------
C. Study operation of system and determine whether compensation is
required to meet performance ^cais without saturating pressures.
D. Determine the effects of variation of parameters.
The block diagram of the mathematical model used for computer simulation is shown
in Figure AII-7. The significant nonlinearities of the engine, vehicle, and hydro-
static transmissions are included in this model. Only those transmission lossao
affecting dynamics were included.
The control functions were partially linearized, since the control configuration
was not established at the time of the computer study.
The system was simulated on an Applied Dynamics AD/4 Analog Computer.
The secondary control system was initially observed to be unstable for all values
of gain K,. This instability resulted from two integrations within the secondary
control system. The first integration is performed by the secondary piston
actuator and the second by the flywheel. These two integrations provide 180
degrees phase lag at all frequencies, and thus result in instability. A
mechanical feedback linkage around the secondary piston actuator was then simu-
lated to reduce the phase lag of this integration. This feedback corrected the
instability. Performance was not satisfactory however. When the secondary
piston actuator acts as an integrator, the flywheel speed will continuously
change as long as a kinetic energy error exists. With the feedback linkage,
integration is no longer performed by the secondary piston actuator. A large
kinetic energy error is then required to obtain a significant change in flywheel
speed. It is necessary to have a significant kinetic energy error at all speeds
to obtain a steady-state value of D,. Therefore, the feedback linkage was con-
sidered unsatisfactory.
Pressure feedback from the secondary hydrostatic transmission 'around the secon-
dary piston actuator was then simulated. The use of pressure feedback with
appropriate values of the gain parameters eliminated the instability in the
secondary control system which occurred as a result of the double integration.
11-12
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ACCELERATOR
PEDAL
Fig. AII-7 Full-Range Block Diagram - Engine Flywheel
Propulsion System
KTI-12539
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The Typo A control, system was then inveni igaued. The Type A control system
utilizes ,-in output speed governor for computing vehicle kinetic energy as
i 11 us trau-.cl in Figure D-3, page D-6 . The output speed input to the secondary
rontrol system forms a positive feedback, or regenerative, type of control loop.
When the secondary control system gain, K , was too high, the system was diffi-
cult to control at high vehicle speed. Once the vehicle speed started to in-
crease, it would continue to increase until the computer overloaded. Returning
the accelerator pedal to zero would not stop this runaway condition. It was
possible to bring the system under control by depressing the brake pedal.
Reducing K eliminated the runaway condition at high vehicle speed. However,
with reduced K, gain, the transient response at low vehicle speed was too slow.
Several methods of eliminating the regenerative condition at high speed without
reducing the transient response at low speed were considered.
One possible method is to schedule gain K as a function of vehicle speed. At
low speed, K^ would be high to obtain good transient response. At high speed,
K would he reduced as required for stable operation.
The square function in the output speed input to the secondary loop is the cause
of the gain variation. The effective gain of this input is proportional to out-
put speed as a result of the square function. Eliminating the square function
would eliminate the variable gain and a constant value of K, could be used at all
speeds. However, with this control configuration, flywheel speed would decrease
Linearly with increasing vehicle speed. The total kinetic energy would then vary
with vehicle speed.
Several other approaches were also considered. However, with any of these
approaches, the positive feedback loop seemed objectional. An unexpected gain
variation could possibly lead to loss of control. Therefore, the B-type control
system configuration shown in Figure D-4, page D-6 , was selected in preference
to the A-type.
The B-type control system uses scheduled vehicle velocity as a function of
accelerator pedal position for the input to the secondary control system. The
11-14
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positive feedback loop, which is the major problem with the A-type control, do is
not exist in the B-type control.
The primary control system gain determined in the linear stability analysis was
found to be the optimum value. The secondary control gains used were a little
lower than the values determined from the stability analysis. The system was
stable with these gain values.
The computer study indicated that some type of dynamic compensation was required
in order to achieve the desired acceleration rates without exceeding the pressure
limits. When fuel flow increases too rapidly, the engine leads the flywheel.
Engine lead results in engine power being used to accelerate the vehicle, and
also can result in the flywheel accelerating during a vehicle acceleration.
When flywheel torque increases too rapidly, excessive vehicle acceleration and
pressure saturation can occur.
Several compensation techniques were investigated, including lagged accelerator
pedal input signal, and lagged fuel flow. The best results were achieved with
dynamic compensation of fuel flow and the secondary piston actuator. These
dynamic compensators effectively modulate the fuel flow and secondary actuator
rate limits to achieve the desired acceleration rates without pressure satura-
tion. There are several possible sources for the input signals to the dynamic
compensators, including primary piston actuator displacement, primary piston
actuator differential pressure, secondary piston actuator displacement, and fuel
flow. The signals from each of these sources appeared to be effective in modu-
lating the dynamic compensators. A more detailed study is required to select the
dynamic compensator input function.
Conclusions
1. Pressure feedback from the secondary hydrostatic transmission around
the secondary piston actuator is required to stabilize the secondary
transmission.
2. The use of an output governor for computing vehicle kinetic energy
is undesirable. This input to the secondary control forms a positive
feedback loop with resulting control problems.
11-15
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3. Dynamic compensation of the fuel flow and secondary piston actuator
is required.
4. The system is stable and is capable of meeting the performance goals
with the gain values selected and with dynamic compensation of fuel
flow and secondary piston actuator.
11-16
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NOMENCLATURE
D displacement of hydrostatic unit, in /rad
2
F, gain of hydrostatic unit A cam block, in
2
F gain of hydrostatic unit 3 cam block, in
2
J inertia, ft Ib sec
K_ primary control system gain, in/sec/rpm
K. gain parameter
K gain parameter, in/sec/ft Ib
2
K gain of hydrostatic unit 1 cam block, in
K pressure feedback gain, in/sec/psi
P
3
L primary hydrostatic transmission leakage parameter, in /sec/psi
3
L secondary hydrostatic transmission leakage parameter, in /sec/psi
N speed, rad/sec
P primary hydrostatic transmission pressure, psi
P secondary hydrostatic transmission pressure, psi
3
Q flow rate, in /sec
R transmission ratio
S d/dt, I/sec
T engine time constant (J 3N/8T),.sec
T compressibility time constant (V/LB), sec
3N/3T reciprocal of slope of engine torque-speed curve, I/ft Ib sec
Subscripts (except as noted in Nomenclature)
e engine
f flywheel
11-17
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o primary transmission output
1 hydrostatic unit 1
2 hydrostatic unit 2
3 hydrostatic unit 3
4 hydrostatic unit 4
11-18
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