Content uploaded by R. Ghafoori-Ahangar

Author content

All content in this area was uploaded by R. Ghafoori-Ahangar on May 28, 2019

Content may be subject to copyright.

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

[1] A. Stokes, Manual Gearbox Design, Society of Automotive Engineers,

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

Technology (Second Edition), 2002, 60-97.

[4] M.S. Abbes, S. Bouaziz, F. Chaari, M. Maatar and M. Haddar, An

acoustic–structural interaction modelling for the evaluation of a

gearbox-radiated noise, International Journal of Mechanical Sciences, 50

(2008), 569-577.

[5] S.L.T. Souza, I.L. Caldas, R.L. Viana, A.M. Batista, T. Kapitaniak,

Noise-induced basin hopping in a gearbox model, Chaos, Solitons & Fractals,

26 (2005), 1523-1531.

[6] G. Lucente, M. Montanari, C. Rossi, Modelling of an automated manual

transmission system, Mechatronics, 17 (2007), 73-91.

[7] C.W. Coon, C.D. Wood, Improvement of Automobile Fuel Economy,

Society of Automotive Engineers, Paper No. 740969 (1985), p. 18.

[8] Engine Research Center, Department of Automotive Engineering, I.A.U.,

Shirgah Branch, Shirgah, Iran.

Received: January, 2010