Vehicle Propulsion Systems
Objectives To introduce mathematical models and optimization methods that allow a systematic minimization of the energy consumption of vehicle systems.
Vehicle A vehicle is a means of transport, such as bicycles, cars, motorcycles, trains, ships, and aircraft. Vehicles that do not travel on land are often called crafts, such as watercraft, sailcraft, aircraft, hovercraft and spacecraft. Most land vehicles have wheels.
Scope of the vehicle: Passenger cars 1. Autonomous 2. Refuelling time short 3. Transport 2-6 people 4. Acceleration 10-15 seconds to 100km/h, and 5%ramp at legal top speed
Modelling of Automotive Systems 1 Powertrain A group of components that generate power and deliver it to the road surface, water, or air, including the engine, transmission, driveshafts, differentials, and the final drive (drive wheels, caterpillar track, propeller, etc.).
The vehicle Powertrain consists primarily of •The Engine (Shown in orange), typically Diesel or Gasoline, but other combustion concept exist or are on the “horizon”. •The Transmission (Shown in green), either a manual, automatic, continuously /infinitely variable transmission, or a hybrid Powertrain with additional electrical components! •After-treatment Systems such as catalysts or particulate traps (Shown in blue) •Electronic Control Units (ECU) and Control Software
EPSRC
Modelling of Automotive Systems 2 On-board energy carrier requirements High energy density Safe and no environmental hazards in production or operation.
Energy sources Hydrocarbons: petroleum (Fossil/mineral or biofuel) , coal, and natural gas Hydrogen – fuel cell Batteries
Biofuel (agrofuel) can be broadly defined as solid, liquid, or gas fuel consisting of, or derived from biomass.
Biomass is grown from plants, including miscanthus, switchgrass, hemp, corn, poplar, willow and sugarcane
Modelling of Automotive Systems 3 Vegetable Oil Fuel
To reduce the viscosity, biodiesel recipe: 1. 1 litre of vegetable oil. 2. 200 millilitres of methanol (95% pure). 3. 5 grams of sodium hydroxide.
Vegetable Oil Fuel Heaters Vegetable Oil is much thicker than mineral diesel at typical ambient temperatures. Therefore, if a vehicle is to be powered by vegetable oil, the oil must be heated before it reaches the fuel filter and the engine's injectors,
Modelling of Automotive Systems 4 3 energy conversion steps:
- well to tank
- tank to vehicle
- vehicle to miles
Modelling of Automotive Systems 5 PP-power plant
Modelling of Automotive Systems 6 Energy Densities
• From tank to wheel energy • CNG-compressed natural gas
Modelling of Automotive Systems 7 Batteries as ‘fuel’
Electrochemical on-board energy carriers -Batteries have low density. Used as auxiliary energy storage to improve IC efficiency (hybrid)
• Lead-acid 30Wh/kg • Nickel-metal hydrides 60Wh/kg • ‘hot’ batteries 150Wh/kg (such as sodium-nickle chloride ‘zebra’ battery) • Improvements are slow • Take long time to ‘refuel’
Modelling of Automotive Systems 8 Pathway to better fuel economy
• Improve well to tank efficiency by optimizing upstream processes
• Improve tank to wheel efficiency by 1. improve the peak efficiency of components 2. improve the part load efficiency 3. recuperate kinetic and potential energy in the vehicle 4. control propulsion system configuration • Improve wheel to mile efficiency by reducing the vehicle mass and aerodynamic and rolling losses
Modelling of Automotive Systems 9 Vehicle Energy
• Kinetic energy when have speed
• Potential energy when have altitudes
Vehicle Energy Losses (after engine)
• Aerodynamic drag • Rolling friction • Brake dissipation
Modelling of Automotive Systems 10 Forces acting on vehicle on motion
Courtesy L.Guzzella et al
dv(t) m = F (t) − (F (t) + F (t) + F (t) + F (t)) v dt t a r g d where
Ft (t) : prime _ mover _ force
Fa (t) : aerodynamic _ friction
Fr (t) : rolling _ friction
Fg (t) : gravity _ force _ component
Fd (t) : other _ disturbance _ force
Modelling of Automotive Systems 11 Aerodynamic Friction
1 F (v) = ρ A c v2 a 2 a f d
Rolling Friction
Fr (v, pt ,...) = cr (v, pt ,...)mv g cos(α)
cr : rolling _ friction _ coefficient
pt :tyre _ pressure ...: road _ surface _ condition,etc
Modelling of Automotive Systems 12 Gravity force component
Fg (v) = mv g sinα
Inertia resistance in rotary parts
dω (t) Total _ inertia _ torque _ of _ wheels : T (t) = Θ w m, w dt
Tm, (t) Additional _ inertia _ force : Fm, (t) = rw where rw : wheel _ radius, using v(t) = ω w (t)rw
Θw dv(t) ω Fm,ω (t) = 2 ω rw dt
Θw Wheel _ inertia : mr,w = 2 rw
Modelling of Automotive Systems 13 Total _ inertia _ torque _ of _ engine
ω Tm, (t) Additional _ inertia _ force : Fm, (t) = rw γ γω ω d e (t) d dv(t) Tm, (t) = Θe = Θe ()γ w (t) = Θe dt dt ω rw dt ω where = gear _ ratio γ Therefore,total _ inertia _ force _ of _ engine 2 γ dv(t) Fm,ω (t) = Θe 2 rw dt 2
mr,e = 2 Θe rw Equivalent _ mass _ of _ rotating _ parts : 2 Θw γ mr = mr,w + mr,e = 2 + 2 Θe rw rw
Modelling of Automotive Systems 14 dv(t) ()m + m = F (t) − (F (t) + F (t) + F (t) + F (t)) v r dt t a r g d where Θ γ 2 m = w + Θ r 2 2 e rw rw
Ft (t) : prime _ mover _ force
Fa (t) : aerodynamic _ friction
Fr (t) : rolling _ friction
Fg (t) : gravity _ force _ component
Fd (t) : other _ disturbance _ force dv(t) Regard F = m as resistance m r dt dv(t) m = F (t) − ()F + F (t) + F (t) + F (t) + F (t) v dt t m a r g d
Modelling of Automotive Systems 15 Performance and Drivability
z Top speed
z Maximum gradient at which vehicle reaches legal top speed
z Acceleration time to 100km/h (60miles/h)
Top speed power (aerodynamic resistance dominant)
1 P ≈ F v = ρ A c v3 max a max 2 a f d max
Modelling of Automotive Systems 16 Performance and Drivability
Uphill driving power
Pmax ≈ vminmv gsinαmax
Modelling of Automotive Systems 17 Performance and Drivability
Energy required to accelerate the vehicle from 0 to v0 (estimate) 1 E = m v2 0 2 v 0 Let mean power
E0 P = t0 Take P P = max 2
Time required to accelerate the vehicle from 0 to v0 E m v2 t = 0 = v 0 0 P Pmax e.g. t0 =10seconds, m v2 1000kg ×(100,000m / 3600s)2 P = v 0 = = 77.16KW =103.6HP max t0 10s
Modelling of Automotive Systems 18 Vehicle Operating Modes
When coasting on horizontal road and without disturbances
dv(t) 1 2 mv = − ρa Af cd v (t) − mv gcr dtρ 2 or
dv(t) 1 2 = − a Af cd v (t) − gcr dt 2mv or β β dv(t) 2 2 2 = − 1 v (t) − 2 βdt where ρ 1 1 = a Af cd , β2 = gcr 2mv
Modelling of Automotive Systems 19 β Vehicle Operating Modes
βWhen coasting on horizontal road and without disturbances β 2 1/ 1 2 dv(t) = −dt 2 2 v (t) + β 1 v 1 v 1 t 1 t Integration : β dv(t) = − dt, 1 arctan 1 v()t = −t β 2 ∫v 2 ∫0 2 0 0 1 β 1 2 2 v β v2 (t) + 2 β 0 β β 1 β β β 1 1 β β arctan v()t −arctan v()0 =β− 1 2t β 2 2 β β () β 2 1 ()β v t = tanarctan v 0 − 1β2t 1 2
This is a slop with negative gradient – coasting gradient
Modelling of Automotive Systems 20 Vehicle Operating Modes
When coasting on horizontal road and without disturbances
dv(t) 1 m β = − ρ A c v2 (t) − m gc v dt 2 a f d v r β β β v()t = 2 tanarctan 1 v()0 − β β t 1 2 1 2
3 operating modes can be identified from the vehicle speed curve
Traction mode: gradient > coasting gradient Braking mode: gradient < coasting gradient Coasting mode: gradient = coasting gradient
Modelling of Automotive Systems 21 Example : For a full size vehicle 2 mv = 1500kg, Af cd = 3.5× 0.2 = 0.7m ,cr = 0.013,v0 = 100km / h = 27.78m / s 1 1 β = A c = 1.2×3.5× 0.2 = 0.0167 1 2m a f d 2×1500 ρv
β 2 = gcr = 9.8× 0.013 = 0.3569 v(t) = 21.37 tan()arctan()0.0468 ×100000 / 3600 − 0.0060t or () v(t) = 21.37 tan 0.9151 − 0.0060t m / s
Coasting velocity 30
25
20
15
v (m/s) 10
5
0
-5 0 20 40 60 80 100 120 140 160 t (s)
Modelling of Automotive Systems 22 Coasting velocity 120
100
80
60
v (km/h) 40
20
0
-20 0 20 40 60 80 100 120 140 160 t (s)
Modelling of Automotive Systems 23 Vehicle Operating Modes
z Traction
Ft > 0
z Braking
Ft < 0
z Coasting
Ft = 0
L.Guzzella et al
Modelling of Automotive Systems 24