Fuel Consumption and Gearbox Efficiency in the Fifth Gear Ratio of Roa Vehicle

Abstract

In this paper, the gear ratio of gearbox in Roa vehicle (An Iranian made car combination of Paykan and Peugeot 405 by Iran Khodro Co.) is computed with considering fuel economy and gearbox efficiency. Firstly, overdrive advantages and its effect on engine rotational velocity have been investigated by consideing road load and engine torque. It is distinguished that in a specified velocity of vehicle, engine speed in overdrive state is very lower than engine speed in fourth gear. It means that noise and fuel consumption and engine wearing and damages will be decreased. The optimized region of engine operation is identified by using a geometric progression between automotive gear ratios and entering effective parameters such as specific fuel consumption, minimum mean effective velocity, and etc. in the formula to compute overdrive gear ratio. Finally, the most appropriate overdrive gear ratio and the number ratio of pair gears are chosen and it is functionally the effective automobile operation.

Full text

Adv. Theor. Appl. Mech., Vol. 3, 2010, no. 7, 299 - 308
Fuel Consumption and Gearbox Efficiency in
the Fifth Gear Ratio of Roa Vehicle
R. Ghafoori-Ahangar
Department of Mechanical Engineering, Iran University of Science and
Technology, Narmak, Tehran, 16846, Iran
rghafooria@Gmail.com
M. R. Meigounpoory
Entrepreneurship Faculty, Tehran University, Tehran, Iran
A. Eskandari
Department of Engineering, University of Mohaghegh Ardabili, Ardabil, Iran
Abstract
In this paper, the gear ratio of gearbox in Roa vehicle (An Iranian made car
combination of Paykan and Peugeot 405 by Iran Khodro Co.) is computed with
considering fuel economy and gearbox efficiency. Firstly, overdrive advantages
and its effect on engine rotational velocity have been investigated by consideing
road load and engine torque. It is distinguished that in a specified velocity of
vehicle, engine speed in overdrive state is very lower than engine speed in fourth
gear. It means that noise and fuel consumption and engine wearing and damages
will be decreased. The optimized region of engine operation is identified by.
Using a geometric progression between automotive gear ratios and entering
effective parameters such as specific fuel consumption, minimum mean effective
velocity, and etc. in the formula to compute overdrive gear ratio. Finally, the most
appropriate overdrive gear ratio and the number ratio of pair gears are chosen and
it is functionally the effective automobile operation.
Keywords: Gear ratio, Fuel economy, Gearbox efficiency, Overdrive, Optimized
region of engine operation

300 R. Ghafoori Ahangar, M. R. Meigounpoory and A. Eskandari
Nomenclature
An photographed surface of the automobile
Cd drag coefficient
F
x
propulsive force
N
f
gear ratio of differential
N
t
gear ratio of gearbox
R resistance force against the automobile movement
RL resultant torque of the resistance force
Te engine torque
Tw effective torque on the wheels
V automobile speed
W automobile weight
n rpm of the engine
r radius of the automobile wheel
f
η
differential efficiency
t
η
gear efficiency
θ
angel of the road slope
ρ
air density
μ
revolving friction coefficient of the road
1. Introduction
Automotive designers thought is affected by two main factors including
increased value of consumed fuel and the competition market of automobiles,
both unit price and supplied facilities are affected. Using the overdrive gear is a
necessity to eliminate the first factor, provided that the fuel economy consumption
is effectively controlled. The second factor has impelled the automobile
manufacturers to produce low cost five-speed gearboxes. To increase output
revolution of the gearbox than that of input revolution a heliacal gearbox system
can be used. In addition, the revolution can be increased by adding a pair of gears
in the gearbox as the fifth gear. Five-speed gearboxes are appropriate alternatives
to be replaced as it is concerned with the fuel economy [1], but the disadvantage is
that application of the fifth gear depends on the driver and it is just used for high
speeds. Overdrive is a device to increase revolution per minute of a low speed
engine [1-3]. The device is used in ordinary gearboxes as the fifth gear with lower
rates of gear, the engine life increase and its noise is reduced due to the reduced
revolution [4-6]. Fuel economy which is very important in automobile
manufacturing industry [6,7] has motivated the automobile industry to develop
methods to reduce the fuel consumption. Performed studies [1-3] indicate
importance of the fuel economy and coordinated gearbox design with the engine
specifications.

Fuel consumption and gearbox efficiency 301
In this research, a new overdrive gear ratio is introduced for four-speed
gearbox of Roa vehicle; the car is a combination of Paykan and Peugeot 405 and a
developed version of the Peugeot RD. Engine speed in fourth gear and engine
speed in overdrive state are compared. With coordinated gearbox and the engine
specification, effective gear rate of the automobile gearbox obtained by the
investigators. The optimized region of engine operation is identified.
2. Mathematical model of the automobile gear ratio
Obtained power from the engine fuel ignition is used to overcome the
resistance forces such as friction forces of the moving components, revolving
resistance of the wheels on the sloped road, and air resistance. When the above
mentioned forces have constant effect, for instance, during fast automobile
moving on plane roads, the forces are able to move the automobile without any
other additional force. With changing the effect of the above mentioned factors
and motion from equilibrium, the engine can not produce the required moment
itself to move the wheels and the engine torque should be changed to an
appropriate rate. Thus, the relation of the engine torque and the effective moment
on the wheels is calculated as follows:
tftfew NTT
η
..= (1)
where Tw is the effective torque on the wheels, and Te is the engine torque; then
Ntf and tf
η
are obtained by the following formula:
fttf NNN .= (2)
fttf
η
η
η
.=
(3)
Nt is the gear ratio of gearbox; Nf is the gear ratio of differential; t
η
is the gear
efficiency and f
η
is the differential efficiency. Ratio of the last gear, for instance
ratio of the forth gear in four-speed gearboxes is assumed to be 1:1 and the ratio
of other gears is obtained by using resistant force (R) based of Fig. 1, since drag
force is zero at the starting movement then the following function is used:
θ
μ
θ
WCosWSinR += (4)
W is the automobile weight;
θ
is the angle of road slope; and
μ
is revolving
friction coefficient of the road, when the Fx propulsive force is:
r
T
Fw
x= (5)
r is radius of the automobile wheel; the propulsive force must be equal or more
than resistance force:

302 R. Ghafoori Ahangar, M. R. Meigounpoory and A. Eskandari
RFx≥
(6)
R
r
NT tftfe ≥
η
..
(7)
Fig. 1. Resistance force on the road slope
When ith gear ratio of the gearbox is shown by Nti and it is assumed that
increased engine moment ((Te)max) is used at the start, then the following formula
is used for the mentioned gear of the gearbox:
R
r
NNT tfftie ≥
η
..)( max (8)
then
tffe
ti NT
rR
N
η
..)( .
max
≥ (9)
According to the catalogue of the manufacturer, the above mentioned formula
of the gearbox is defined as follows [8]:
07197434.0 ,98.0 ,95.0 ===
f
ft N
r
ηη
(10)
To calculate (9) relation, we need to know the increased torque of the engine;
when the curve of engine moment has been obtained by changing revolution of
the engine Roa; chassis and drive train are similar to the older Paykan but the
outer body shell and appearance resemble a Peugeot 405 and it is made by Iran
Khodro Co. According to Fig. 2:
θ
μW Cosθ
W Sinθ

Fuel consumption and gearbox efficiency 303
)N.m( 82.109)lbf.ft( 81)( max ==
e
T (11)
50
60
70
80
90
0 1000 2000 3000 4000 5000 6000
n(rpm)
Engine torque(lbf.ft)
Tave.
Tmin
Tmax
Fig. 2. Torque curve of the Roa automobile engine
If the maximum sine of the road is 33% and allowable weight of automobile is
W= 13538 N and revolving friction coefficient of rubber and asphalt is µ=0.0248
[8] according to equation (4) we will have: 1.4783)94.0()13538()0248.0()33.0)(13538(
=
×
×+=RN (12)
By replacing values from equation (10) and increased torque of the engine
from above diagram according to the values of equation (11) and resistant force of
equation (12) in equation (9), simplification of Nti is amendable by the following
equation: 367.3)1.4783)(1004.7( 4=×≥ −
ti
N (13)
Since the four-speed gear ratio of automobile is 3.353, probably the little
difference is due to the primary hypothesis including allowable weight, friction
coefficient and so forth.
Some of the researchers believe that gear ratios of the automobile gearbox are
calculated by a geometric progression and q modulus [1-3]. According to gear
ratios 1 and 4, the progression is defined as follows:
3
1qNt=,2
2qNt=, qNt=
3, and 1
4
=
t
N (14)
therefore
4967.1
24.2)4967.1(
4967.1)353.3()(
3
22
2
3
1
3
1
1
==
===
===
qN
qN
Nq
t
t
t
(15)
Ratio of automobile gears and obtained results of Nt1=3.353 and Nt1=3.367 are
compared in Table 1.

304 R. Ghafoori Ahangar, M. R. Meigounpoory and A. Eskandari
Table 1. Comparison of current gear ratios of Roa automobile and calculated
amounts in the study
Nt1 Nt2 Nt3 Nt4
Ratio of automobile gears 3.353 2.141 1.392 1
Ratio of gears by using Nt1=3.353 3.353 2.24 1.497 1
Ratio of gears by using Nt1=3.367 3.367 2.246 1.498 1
The above mentioned results have been computed by a geometric progression
and when Nt1=3.353 is used, the gear ratio is increased five times:
66.0
4967.1 11
5=== q
Nt (16)
The gear ratio is modified by considering some parameters such as the specific
fuel consumption and by changing minimum effective speed. Firstly the above
mentioned parameters are defined and then the concerning curves are drawn.
According to the equation (4), primary air resistance force is assumed to be zero
and then the resultant forces are calculated based on the following formula:
2
2
1VACWCosWSinR nd
ρθμθ
++= (17)
V is the automobile speed; ρ is the air density; Cd is the drag efficiency; An is the
photographed surface of the automobile, if the road load (resultant torque of
resistance force) is shown by RL, according to equations (7) and (17), the formula
would be:
)
2
1
(
.. 2
VACWCosWSin
N
r
N
R
rRL nd
tftftftf
ρθμθ
ηη
++×=×= (18)
The torque of automobile is reduced when RL≥Tw, but it is increased when
RL<Tw
and it is remained constant when RL=Tw, that are clearly shown in Fig. 3.
Accordingly engine torque depends on the drag coefficient and according to
equation (18); the increased speed of the automobile is contrary to the drag
coefficient.
0
25
50
75
100
1000 2000 3000 4000 5000
n(rpm)
Ibf.ft
Road load
Engine torque
Fig. 3. Confluence curve of the road load and engine torque

Fuel consumption and gearbox efficiency 305
3. Effective operation limit of the automobile
Effective operation limit of the automobile depends on the following items:
 According to Fig. 3, the increased speed of the automobile is contrary to the
drag coefficient, thus the coefficient is possibly decreased with effective
aerodynamic.
 According to this Figure, since the road load and the engine torque are
increased where the two curves are intersected but then the engine torque is
decreased, it is an indication of a limited speed.
 According to Fig. 4, if engine torques of A and B are considered the same
respectively before and after the increased engine torque, every preventing
factor may reduce speed of the automobile, but the torque is increased at B to
defuse the effect of preventing factor, thus speed and revolution of the engine
must be located after the increased torque of the engine.
 According to Fig. 4, it must be approached to the increased power of the
engine.
 According to the above mentioned items, the best operation limit is almost the
difference of increased engine torque and increased power of the engine.
Fig. 4. The effective operation limit of the automobile
4. Results and Discussion
Automobile velocity (V, km/h) is based on the engine n (rpm) of the fourth
gear when the overdrive gear ratio is 1:1 and the gear ratios are 0.81 and 0.84,
they are shown in Fig. 5. The curve has indicated the important advantage of the
overdrive.

306 R. Ghafoori Ahangar, M. R. Meigounpoory and A. Eskandari
0
50
100
150
200
1000 2000 3000 4000 5000
n(rpm)
V(km/h)
1
0.84
0.81
Gear ratio
Fig. 5. Diagram of engine velocity change (V, km/h) in n (rpm) of the fourth gear
with 1:1 gear ratio and 0.81 and 0.84 overdrive ratio
If we study a specific output velocity of an engine, for instance in 120 km/h,
then the fourth rpm is 4600 but with 0.81 and 0.84 overdrive gear ratios it is
respectively 3530 and 3600 rpm that is almost 1000 rpm lower than that of the
forth gear that results in noise reduction and friction reduction of the engine.
Fig. 6 shows road torque diagram based on different overdrive gear ratio and
the force gear. The mid point of the road torque curve and the engine torque curve
will be the same as the cars limited speed. It is obvious from diagram that with
reducing of round gear ratio, cars limited speed reduces (under design condition).
0
20
40
60
80
100
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
n(rev/min)
Road load(lbf.ft) Torque(lbf.ft)
100
80
60
40
20
.64 .7 .76 .8
.81
.84 1
Fig. 6. Road torque diagram based on different overdrive gear ratios and the
fourth gear
Table 2 depicts the maximum and minimum output velocity of the automobile
with different overdrive gear ratios. According to the data, the minimum velocity
increases when the gear ratio is decreased, and in gear ratio of 0.71 and less, the

Fuel consumption and gearbox efficiency 307
ratio of maximum velocity is decreased that is an indication of impossible
overdrive use. Besides, Table 2 is an indication of appropriate gear ratio of the
pair gears, when the appropriate gear is selected according to the Table. Fig. 7
shows the arrangement of the designed and developed models of gearbox.
Table 2. Ratio selection procedure of the overdrive gear
N
t
1 0.84 0.81 0.8 0.79 0.76 0.7 0.64
Velocity Specific fuel consumption
80 0.272 0.268 0.270 0.272 0.273 0.276 0.285 0.293
90 0.270 0.270 0.267 0.267 0.268 0.268 0.273 0.282
100 0.268 0.272 0.272 0.272 0.271 0.270 0.267 0.272
110 0.268 0.269 0.270 0.271 0.271 0.272 0.270 0.268
120 0.273 0.267 0.271 0.269 0.269 0.270 0.272 0.270
Max. Velocity 131 124 123 122 120 118 112 102
rpm of the Engine 4900 3850 3700 3600 3500 3350 2900 2450
Min. Velocity 75.97 90.45 93.80 94.97 96.17 99.97 108.5 118.7
Fig. 7. Gearbox arrangement of the designed and developed models
New pair gears

308 R. Ghafoori Ahangar, M. R. Meigounpoory and A. Eskandari
5. Conclusion
A new overdrive gear ratio is introduced for four-speed gearbox of Roa (An
Iranian made car combination of Paykan and Peugeot 405 by Iran Khodro Co.). If
the engine works with lower ratios or 0.79, we notice that the consumption of
specific fuel is increased compared with 0.8 to 0.84. According to the above
mentioned results the appropriate gear ratio must be 0.8 to 0.84. Based on the
minimum engine rpm, 0.8 is the appropriate gear ratio. Number of 0.8 (0.64-1)
gear ratios and appropriate pair gears were studied according to Table 2 with trial
and error procedure; the general effect of fuel economy parameters were
evaluated; minimum engine velocity, the difference of maximum and minimum
effective velocity of the engine were studied to specify 0.81 as the most
appropriate engine ratio, finally the number ratio of pair gears are 19 to 34, and it
is functionally the effective automobile operation.
References
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Butterworth-Heinemann Ltd., 1992, 176 pages.
[2] G. Lenchner, H. Naunheimer, Automotive Transmission, Springer Ltd.
(2005), 70-95.
[3] H. Heisler, Manual gearboxes and overdrives, Advanced Vehicle
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[4] M.S. Abbes, S. Bouaziz, F. Chaari, M. Maatar and M. Haddar, An
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(2008), 569-577.
[5] S.L.T. Souza, I.L. Caldas, R.L. Viana, A.M. Batista, T. Kapitaniak,
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Shirgah Branch, Shirgah, Iran.
Received: January, 2010