A heavy truck has the following engine-power train properties: Engine rotational
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Question
A heavy truck has the following engine-power train properties: Engine rotational inertia = 2.4 kg-m- Transmission rotational inertia 3.9 kg-m2 Transmission (first gear) ratio = 7.53 Driveshaft / final drive rotational inertia = 3.5 kg-m2 Combined rotational inertias of all wheels = 210 kg-m2 Final drive (rear end) ratio Tire radius = 0.5 m . · . 4.11 · What is the effective mass of the rotating components when in first gear? The truck in the previous problem weighs 36,000 kg when loaded. At 2000 RPM its engine can produce a torque of 1150 N-m. For these conditions, determine the vehicle forward speed and its acceleration capability in first gear, assuming an overall driveline efficiency of 90% (neglect aerodynamic, rolling resistance, grade, and towing forces).Explanation / Answer
Air Resistance (Air Drag) (AR):
where:
AR = air resistance [N]
= air density [kg/m3] 1.202 kg/m3, at sea level and at 15o C
Af = car frontal area [m2] 1.2 : 3.2 m2, for small and mid size cars
Cd = coefficient of aerodynamics resistance (drag coefficient) 0.2 : 0.5 for cars
v = car relative velocity [km/h]
vcar = car velocity [km/h] (vcar = v, at stand still wind, vwind = 0)
vwind = wind velocity [km/h]
* ( + ), (+) with head wind, the wind velocity opposite the car velocity direction (against) .
(-) with tail wind, the wind velocity in the same direction as the car velocity (with).
Rolling Resistance (RR):
where:
RR = rolling resistance [N]
fr = coefficient of rolling resistance 0.015 : 0.02 (hard surface) 0.2 : 0.3 (sand)
w = car weight [N] 10000 : 24000 N, for small and mid size cars
m = car mass [kg] 1000 : 2400 kg, for small and mid size cars
g = acceleration due to gravity = 9.81 [m/s2]
Gradient Resistance (GR):
where:
GR = gradient resistance [N]
w = car weight [N] = mg [kg m/s2, (N)]
= gradient angle < 2.3o (highways), 5.7 : 6.9o (local roads), 11.5o (max. grad)
S = gradient percentage [%]
S < 4% (highways), <10% : 12% (local roads), 20% (maximum gradient)
G = gradient ratio [1: n = 1/n]
<1:25 (1/25) highways, < 1:8 (1/8) local roads, 1:5 (1/5) maximum grad.
* ( + ), (+) with the car going up hill (ascending). {resistance effort}
(-) with the car going down hill (descending). {tractive effort}
Inertia Resistance (IR):
where:
IR = inertia resistance [N]
m = car mass + equivalent mass of rotating parts [kg]
a = car acceleration [m/s2], (from 0 to 100 km/h in: 6 s (4.63 m/s2), 18 s (1.543 m/s2))
mcar = car mass [kg]
meq = equivalent mass of rotating parts [kg]
= [ Iw (1/rw)2 + Ip hf (if /rw)2 + Ie ht (if ig / rw)2]
where:
Iw = polar moment of inertia of wheels and axles 2.7 [kg m2]
Ip = polar moment of inertia of propeller shaft 0.05 [kg m2]
Ie = polar moment of inertia of engine 0.2 [kg/m2] + polar moment of inertia of flywheel and clutch 0.5 [kg m2]
hf = mechanical efficiency of final drive
ht = mechanical efficiency of transmission system (hg x hf)
ig = gearbox reduction ratio [ig1 or ig2 or ………….]
if = final drive reduction ratio
rw = tire radius [m]
* ( + ), (+) with the car in acceleration. {tractive resistance}
(-) with the car in deceleration. {tractive effort}
Total Resistance (TR):
where:
TR = total resistance [N]
RR = rolling resistance [N]
AR = air resistance [N]
GR = gradient resistance [N]
IR = inertia resistance [N]
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