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,ω w dt Tm,ω (t) Additional _ inertia _ force : Fm,ω (t) = rw where rw : wheel _ radius, using v(t) = ωw (t)rw Θw dv(t) Fm,ω (t) = 2 rw dt Θw Wheel _ inertia : mr,w = 2 rw Modelling of Automotive Systems 13 Total _ inertia _ torque _ of _ engine Tm,ω (t) Additional _ inertia _ force : Fm,ω (t) = rw dωe (t) d γ dv(t) Tm,ω (t) = Θe = Θe ()γωw (t) = Θe dt dt rw dt where γ = gear _ ratio Therefore,total _ inertia _ force _ of _ engine γ 2 dv(t) Fm,ω (t) = Θe 2 rw dt γ 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 2 Θw γ mr = 2 + 2 Θe 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 E P = 0 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 m = − ρ A c v2 (t) − m gc v dt 2 a f d v r or dv(t) 1 2 = − ρa Af cd v (t) − gcr dt 2mv or dv(t) = −β 2v2 (t) − β 2 dt 1 2 where 1 β1 = ρa Af cd , β2 = gcr 2mv Modelling of Automotive Systems 19 Vehicle Operating Modes When coasting on horizontal road and without disturbances 2 1/ β1 2 dv(t) = −dt 2 β2 v (t) + β1 v 1 v 1 t 1 β β t Integration : dv(t) = − dt, 1 arctan 1 v()t = −t 2 ∫v 2 ∫0 2 0 β 0 β β2 β2 1 2 β2 1 v0 v (t) + β1 β1 β1 arctan v()t −arctan v()0 = −β1β2t β2 β2 β β 2 1 v()t = tanarctan v()0 − β1β2t β1 β2 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 = − ρ A c v2 (t) − m gc v dt 2 a f d v r β β v()t = 2 tanarctan 1 v()0 − β β t 1 2 β1 β2 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 β1 = ρa Af cd = 1.2×3.5× 0.2 = 0.0167 2mv 2×1500 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.