Vehicle Tehcnology

7/27/2019 Vehicle Tehcnology

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FWD

Car weight (laden) W 18200N

Wheel base L 2810mm

Center of Gravity l1 1349mm h 702mm l2 L l1 1461mm

Width of vehicle w 1811mm

Unloaded height hcar 1429mm

Aerodynamic drag coef. CD 0.32

Rolling resistant coef f R V( ) 0.0136 0.4 107

V2

hr

2

km2

V : is the speed of the vehicle in km/hr

Transmission efficiency

(Direct Drive) ηt1 0.98

Transmissioni efficiency

(other gears)

ηt 0.95

* tire slip and the inertia of the drive train components are neglected



a) Engine torque and engine power with respect to engine speed

Engine speed (rpm) Engine Torque (N*m) Engine Power (kW)

600 115 10

1000 125 12

1500 148 23

2000 150 30

2500 160 42

3000 167 50

3500 170 64

4000 176 70

4500 185 90

5000 183 100

5500 180 105

6000 170 111

b) Tire selection

W 18200NW

4 g463.971kg

Load index is selected :88

Speed symbol is selected : H for 201 km/hr maximum speed

Selected tire : 185/65 R 15 88 H

Wheel load capacity : 560Dynamic radius of tire : 302 mmr dyn 0.302m



c) Power versus road speed graph (on a level road)

While vehicle moves on a road level θ 0deg r dyn 0.3m a 0

While our tire speed symbol is H, the maximum vehicle speed will be limited by 210 km/hr

Vehicle speed : V 0km

hr 20

km

hr 200

km

hr

Air density : ρair 1.23 kg

m3

Frontal area of vehicle : Af w hcar 2.588m2

Rolling resistance coef : f R V( ) 0.0136 0.4 107

V2

hr

2

km2

Total road resistance force : Fr V( )1

2ρair CD Af V

2 f R V( ) W

Total power required to overcome the road recistances :

Nr Fr V= Nr V( ) Fr V( ) V

0 10 20 30 40 50 600

3 104

6 104

9 104

1.2 105

1.5 105

Required Power vs Vehicle speed

Speed of vehicle m/s

R e q u i r e d P o w e r W

Nr V( )

V



d) The maximum speed this vehicle can reach on a level road

Air density : ρair 1.23kg

m3

Frontal area of vehicle : Af w hcar 2.588m2

Rolling resistance coef : f R

V( ) 0.0136 0.4 107

V2

hr

2

km2

Maxiumum power generated by engine is 111kW @6000rpm

Nemax 111kW nemax 6000rpm

Then traction power is : Ntmax Nemax ηt 105.45 kW

Ntmax1

2ρair CD Af Vmax

3 f R Vmax W Vmax=

Vmax 56.353m

s202.871

km

hr

e) The maximum grade this vehicle can climb without wheel slippage on a dry pavementwhere the traction coefficient is 0.8

μ p 0.8 f R 0.014

Assumptions: R Lf R Lr = 0= a 0= R dx 0= R dz 0=

From the traction limits criteria :

μ p f frontFxf

Wf.

=

W sin θ( ) Wr f R

l2

LW cos θ( )

h

LW sin θ( )

= Rear axle has only rolling resistance

μ p f front Fxf Wf.

=

W sin θ( )l1

L

W cos θ( )h

L

W sin θ( )

f

R

l2

LW cos θ( )

h

LW sin θ( )

=

tan θ( )FWD

l2

Lμ p

l1

Lf R

1h

Lμ p f R

Max. grade the vehicle can climb

Grade

l2

L μ p

l1

L f R

1h

Lμ p f R

0.34 The maximum grade vehicle can climb is %34



f) 4th gear is direct drive and 5th speed is reserved for fuel economy

ξ4 1

Memax 185N m @ n=4500rpm

tan θmax Grade=

ξ1

W tan θmax f R r dyn

Memax ξax ηt 1 tan θmax 2

= Wheel torque / Engien torque

ξ1 ξax ξoverall=

W tan θmax f R r dyn

Memax ηt 1 tan θmax 2

=

ξoverall

W Grade f R r dyn

Memax ηt 1 Grade2

10.414

4th gear is direc drive ξ4 1 i 0 no slip ne 6000rpm

ξ4 ξaxne r dyn 1 i( )

Vmax

= ξax

ne r dyn 1 i( )

Vmax

3.345

ξ1

ξoverall

ξax

3.113

Geometric speed transmission : K g

3ξ

4ξ1

0.685

ξ2 K g ξ1 2.132

ξ3 K g ξ2 1.46

g) 5th gear ratio for the best fuel consumption cruising on a highway at a constant speed of 110 km/hr

be 250g

kW hr V 110

km

hr n 2400rpm

Power required for the best fuel consumption is Nopt 40kW

From vehicle speed formula : Vn r dyn 1 i( )

ξo

= ξo

n r dyn 1 i( )

V2.468

ξ5

ξo

ξax

0.738



h) Graphs of tractive effort w.r.t. the vehicle speed and tractive power w.r.t. vehicle speed forall gear ratios

Tractive effort formula : FMe ξo ηt

r dyn

=

Vehicle speed formula : n 600rpm 650rpm 6000rpm V n( )n r dyn 1 i( )

ξo

V 600rpm( ) 27.5km

hr V 6000rpm( ) 275

km

hr V 27.5

km

hr 28

km

hr 275

km

hr

Tractive power formula : N F V= Me n 1 i( )=

Rolling resistance coef : f R V( ) 0.0136 0.4 107

V2

hr

2

km2

Total road tractive force : Ft V( )1

2ρair CD Af V

2 f R V( ) W

Mt V( ) Ft V( ) r dyn

Me V ξg Mt V( )

ξg ξax ηt

Tractive effort formula : F V ξg Me V ξg ξo ηt

r dyn

0 10 20 30 40 50 60 70 800

1 103

2 103

3 103

4 103

Tractive Effort vs Vehicle Speed

Vehicle Speed [m/s]

T r a c t i v e e f f o r t

F V ξ1

F V ξ2

F V ξ3

F V ξ4

F V ξ5

V



Tractive power formula : N V ξg F V ξg V

0 10 20 30 40 50 60 70 800

5 104

1 105

1.5 105

2 105

2.5 105

3 105

Tractive Power vs Vehicle Speed

Vehicle Speed [m/s]

T r a c t i v e P o w

e r

N V ξ1

N V ξ2

N V ξ3

N V ξ4

N V ξ5

V

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