A vehicle of the following data is equipped with a 4-speed AT. The ratios are: 2.84(1st), 1.60(2nd), 1.0(3rd),

0.7(4th). The final drive ratio is 2.84. The torque converter has the characteristics as shown. The engine

WOT output torque is also shown. The vehicle is being driven on level ground in the first gear with the

torque converter unlocked.

a) Present the differential equation system with the initial condition for the WOT performance simulation

model of the vehicle in the first gear. Assume the vehicle is launched at engine idle RPM.

b)

Determine the engine angular acceleration and vehicle acceleration when the vehicle is just launched

from stand still.

c)

Starting from time zero and using a step size of t=0.2, solve the differential equation system for one

step, i.e., find the engine RPM and vehicle speed 0.2 second after launch.

Vehicle Data

Front axle weight: 1290 lbs

Center of gravity height: 18 inch

Air drag coefficient: 0.31

Tire radius: 10.0 in.

Powertrain efficiency: 0.92

Torque 250

(ft.lb)

200

150

100

50

0

torque

1000 2000

Rear axle weight: 1240 lbs

Wheel base: 100 in.

Frontal projected area: 20 square feet

Roll resistance coefficient: 0.02

Mass moment of inertia of engine-impeller: 0.3 lbs.ft²

Max. Torque

Max Power

3000 4000 5000 6000

237.5 (HP)

190

95

7000

142.5

Power

47.5

Max. Power:

200 нрат 5500 Rem

'Mex, тогдые:

199 ft.bat 3850RPM

RPM/n100

50

TORQUE RATIO

0

2.2

2.0

1.8

1.6

1.4

1.2

1.0

.8

1000

K CAPACITY FACTOR

300

280

260

240

220

200

180

160

140

120

100

80

60

40

20

0

2000 3000

TORQUE RATIO

4000

5000 6000

IMPELLER SPEED-

EFFICIENCY-

PERFORMANCE BASED ON 200 LB. FT.

CONSTANT INPUT TORQUE

SPEED RATIO

7000

100

.9 1.0

90

80

70

60

50

40

30

20

10

0

EFFICIENCY - PERCENT

95

47.5

RPM

3200

3000

2800

2600

2400

2200

2000

1800

1600

1400

1200

1000

800

600

400

200

199 ft.bat 3850RPM

0

IMPELLER SPEED - RPM