resistance forces on a vehicle p m v subbarao professor mechanical engineering department estimation...
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Resistance Forces on A Vehicle
P M V SubbaraoProfessor
Mechanical Engineering Department
Estimation of Vehicle Demands….
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Resistance Forces on A Vehicle
• The major components of the resisting forces to motion are comprised of :
• Acceleration forces (Faccel = ma & I forces)• Aerodynamic loads (Faero) • Gradeability requirements (Fgrade)• Chassis losses (Froll resist ).
maFFFF grraero
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Force System Due to Rolling Resistance
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Road Conditions
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Rolling Resistance
Composed primarily of
1. Resistance from tire deformation (90%)
2. Tire penetration and surface compression ( 4%)
3. Tire slippage and air circulation around wheel ( 6%)
4. Wide range of factors affect total rolling resistance
The magnitude of this force is Approximated as:
Rolling resistance of a vehicle is proportional to the component of weight normal to the surface of travel
gV M C = P rrrr
MgFrr MgCF rrrr
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Standard Formula for Rolling Resistance
V M C )10 (2.72 = P
V M C 3600
9.81 = P
rr3-
rr
rrrr
where:
P
= power (kW)
Crr
= coefficient of rolling resistance
M
= mass (kg)
V
= velocity (KpH)
147101.0
VCrr
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Contact Type Crr
Steel wheel on rail 0.0002...0.0010
Car tire on road 0.010...0.035
Car tire energy safe 0.006...0.009
Tube 22mm, 8 bar 0.002
Race tyre 23 mm, 7 bar 0.003
Touring 32 mm, 5 bar 0.005
Tyre with leak protection 37 mm, 5 bar / 3 bar
0.007 / 0.01
Typical Values of Coefficient of Rolling Resistance
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Effect of Road Condition on Crr
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Rolling Resistance And Drag Forces Versus Velocity
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Grade Resistance
Composed of – Gravitational force acting on the vehicle
gg mgF sin
gg tansin
gg mgF tan
Gg tan
mgGFg
For small angles,
θg mg
θg
Fg
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Total Vehicular Resistance at Constant Velocity
AR = air resistance [N] RR = rolling resistance [N]
GR = gradient resistance [N]TR = total resistance [N]
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Res
ista
nce
Vehicle Speed
Steady State Demand Curve
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Vehicle Speed vs. Engine Speed
o
crank
G
irNV
60000
12
V = velocity , km/hr
r = wheel radius, m
Ncrank = crankshaft rpm
i = driveline slippage
GO = Overall gear reduction ratio
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Typical Engine Torque-Power Curves @ SS
wheel
EE r
TF
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Steady State Demand Vs Available Effort
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Inertial or Transient Forces
• Transient forces are primarily comprised of acceleration related forces where a change in velocity is required.
• These include:• The rotational inertia requirements (FI ) and • the translational mass (Fma). • If rotational mass is added to a translating vehicle, it adds not
only rotational inertia but also translational inertia.
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Inertial Resistance
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a m = F vehicleeffIR
a m m = F eqvehicleIR
where:FIR = inertia resistance [N] meff-vehicle = Vehicle 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))mvehicle = Vehicle mass [kg]meq = Equivalent mass of rotating parts [kg]
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= angular acceleration k = radius of gyration
Equivalent Mass of Rotating Parts
Torque due to any rotating part (ex. Wheel)
wheelwheelwheeli I = dt
d I = T
wheel2
wheel k m =r
a = tire
vehiclewheel
wheels and axles = 78% of total polar inertia propeller shaft = 1.5%Engine = 6%Flywheel and clutch =14.5%
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Therefore the equivalent mass of all rotational parts including losses is represented as:
2
22
2
2
2&
wheel
gbfmtclutchflywheele
wheel
ffpropeller
wheel
axleswheeleq r
GGIII
r
GI
r
Im
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Required Torque & Power at Wheels
wheel
vehicledemandwheel
pT
wheel
vehicledemandwheel N
pT
2
60
wheel
mtenginewheel N
pT
2
60
fgb
engine
mtenginewheel
GGN
pT
2
60
fgb
engine
mtenginewheel
GGN
pP
2
60
mtfgbenginewheel GGTT
wheel
mtfgbengine
wheel
wheelTE r
GGT
r
TF
Tractive Effort demanded by a vehicle):
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Available Vehicle Tractive Effort (TE):
The minimum of:1. Force generated by the engine, Fe2. Maximum value that is a function of the vehicle’s
weight distribution and road-tire interaction, Fmax
max,mineffort tractiveAvailable FFe
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Tractive Effort Relationships
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MATLAB for Vehicle Torque Requirement
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MATLAB Model for Transmission System
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Requirements of Vehicle on Road & Engine Power
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Urban Driving Cycle
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Engine RPM during Urban Driving Cycle
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Engine Fuel Consumption During Urban Driving Cycle