Vehicle Propulsion Systems Lecture 2 Fuel Consupmtion Estimation – The Basics Lars Eriksson Associate Professor (Docent) Vehicular Systems Link¨opingUniversity October 27, 2010 Outline Repetition Energy Consumption of a Driving Mission The Vehicle Motion Equation Losses in the vehicle motion Energy Demand of Driving Missions Other Demands on Vehicles Performance and Driveability Energy demand and recuperation Methods and tools Software tools W2M – Energy Paths Energy System Overview Primary sources Different options for on- board energy storage Powertrain energy conver- sion during driving Cut at the wheel! Driving mission has a mini- mum energy requirement. Outline Repetition Energy Consumption of a Driving Mission The Vehicle Motion Equation Losses in the vehicle motion Energy Demand of Driving Missions Other Demands on Vehicles Performance and Driveability Energy demand and recuperation Methods and tools Software tools Energy Consumption of a Driving Mission I Remember the partitioning –Cut at the wheels. I How large force is required at the wheels for driving the vehicle on a mission? Repetition – Work, power and Newton’s law Translational system – Force, work and power: W = Z F dx , P = d dt W = Fv Rotating system – Torque (T = Fr ), work and power: W = Z Td θ, P = T ω Newton’s second law: Translational Rotational m dv dt = F driv - F load J dω dt = T driv - T load The Vehicle Motion Equation Newton’s second law for a vehicle m v d dt v (t )= F t (t ) - (F a (t )+ F r (t )+ F g (t )+ F d (t )) Ft Fr Fa Fd α mv · g Fg I F t – tractive force I F a – aerodynamic drag force I F r – rolling resistance force I F g – gravitational force I F d – disturbance force
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Vehicle Propulsion Systems Lecture 2 - Fuel Consupmtion ... · Aerodynamic Drag Force { Loss Aerodynamic drag force depends on: Frontal area A f, drag coe cient c d, air density ˆ
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Vehicle Propulsion SystemsLecture 2
Fuel Consupmtion Estimation – The Basics
Lars ErikssonAssociate Professor (Docent)
Vehicular SystemsLinkoping University
October 27, 2010
Outline
Repetition
Energy Consumption of a Driving MissionThe Vehicle Motion EquationLosses in the vehicle motionEnergy Demand of Driving Missions
Other Demands on VehiclesPerformance and DriveabilityEnergy demand and recuperation
Methods and toolsSoftware tools
W2M – Energy Paths Energy System Overview
Primary sources
Different options for on-board energy storage
Powertrain energy conver-sion during driving
Cut at the wheel!
Driving mission has a mini-mum energy requirement.
Outline
Repetition
Energy Consumption of a Driving MissionThe Vehicle Motion EquationLosses in the vehicle motionEnergy Demand of Driving Missions
Other Demands on VehiclesPerformance and DriveabilityEnergy demand and recuperation
Methods and toolsSoftware tools
Energy Consumption of a Driving Mission
I Remember the partitioning–Cut at the wheels.
I How large force is required at the wheels for driving thevehicle on a mission?
Repetition – Work, power and Newton’s law
Translational system – Force, work and power:
W =
∫F dx , P =
d
dtW = F v
Rotating system – Torque (T = F r), work and power:
W =
∫T dθ, P = T ω
Newton’s second law:
Translational Rotational
m dvdt = Fdriv − Fload J dω
dt = Tdriv − Tload
The Vehicle Motion EquationNewton’s second law for a vehicle
mvd
dtv(t) = Ft(t)− (Fa(t) + Fr (t) + Fg (t) + Fd(t))
Ft
Fr
Fa
Fd
α
mv · g
Fg
I Ft – tractive force
I Fa – aerodynamic drag force
I Fr – rolling resistance force
I Fg – gravitational force
I Fd – disturbance force
Aerodynamic Drag Force – Loss
Aerodynamic drag force depends on:Frontal area Af , drag coefficient cd , air density ρa and vehiclevelocity v(t)
Fa(t) =1
2· ρa · Af · cd · v(t)2
Approximate contributions to Fa
I 65% car body.
I 20% wheel housings.
I 10% exterior mirrors, eave gutters, window housings,antennas, etc.
I 5% engine ventilation.
Rolling Resistance LossesRolling resistance depends on:load and tire/road conditions
Fr (v , pt , surface, . . .) = cr (v , pt , . . .) ·mv · g · cos(α), v > 0
The velocity has small influence at low speeds.Increases for high speeds where resonance phenomena start.
Assumption in book: cr – constant
Fr = cr ·mv · g
Gravitational Force
I Gravitational load force–Not a loss, storage of potential energy
Ft
Fr
Fa
Fd
α
mv · g
Fg
I Up- and down-hill driving produces forces.
Fg = mv g sin(α)
I Flat road assumed α = 0 if nothing else is stated (In thebook).
Inertial forces – Reducing the Tractive Force
Te
ωe
Ft
GearboxWheel
Je
Engine Jw
γ
ωw
rw
Tt
Te − Jeddtωe = Tgb Tgb · γ − Jw
ddtωw = Tt
Variable substitution: Tw = γ Te , ωw γ = ωe , v = ωw rw
Tractive force:Ft = 1
rw
[(Te − Je
ddt
v(t)rwγ) · γ − Jw
ddt
v(t)rw
]= γ
rwTe −
(γ2
r2wJe + 1
r2wJw)
ddt v(t)
The Vehicle Motion Equation:[mv + γ2
r2wJe + 1
r2wJw]
ddt v(t) = γ
rwTe − (Fa(t) + Fr (t) + Fg (t) + Fd(t))
Vehicle Operating Modes
The Vehicle Motion Equation:
mvd
dtv(t) = Ft(t)− (Fa(t) + Fr (t) + Fg (t) + Fd(t))
I Ft > 0 traction
I Ft < 0 braking
I Ft = 0 coasting
d
dtv(t) = − 1
2 mvρa Af cd v2(t)− g cr = α2 v2(t)− β2
Coasting solution for v > 0
v(t) =β
αtan
(arctan
(α
βv(0)
)− αβ t
)
How to check a profile for traction?The Vehicle Motion Equation: