Vehicle Propulsion Systems. Tutorial Lecture on 22 nd of Dec.

Transcription

1 Vehicle Propulsion Systems Tutorial Lecture on 22 nd of Dec.

2 Planning of Lectures and Exercises: Week Lecture, Friday, 8:15-10:00, ML F34 Book chp. 38, Introduction, goals, overview propulsion systems and options Exercise, Friday, 12:00-13:30, CHN E46 1 Introduction 39, Fuel consumption prediction I 2 Exercise I, Milestone 1 40, Fuel consumption prediction II 2 Exercise I, Presentation 41, IC engine propulsion systems I 3 Exercise II, Milestone 1 42, IC engine propulsion systems II 3 Exercise II, Milestone 2 43, Hybrid electric propulsion systems I 4 Exercise II, Presentation 44, Hybrid electric propulsion systems II 4 Exercise III, Milestone 1 45, Hybrid electric propulsion systems III 4 Exercise III, Milestone 2 46, Supervisory Control Algorithms I 7 Exercise III, Presentation 47, Non-electric hybrid propulsion systems 5 Exercise IV, Milestone 1 48, Optimal Control Theory AppII&III Exercise IV, Milestone 2 49, Supervisory Control Algorithms II 7 Exercise IV, Milestone 3 50, Case Study Exercise IV, Presentation 51, Tutorial Lecture, Q & A

3 Oral Exams Mode of exam: Chris, Philipp and Student in one room Pencil, paper and calculator, no notes 2 questions, 15min each, (30min in total) 1 question about the first half of lecture, 1 about the second Dates:

4 Exams Prüfungsplankomission will announce final dates in early Chris and Philipp have filled out a plan of availabilities in the time between Jan. 22 nd and Feb. 16: see below. The exams will likely not take place when we have signaled unavailability.

5 Engine Map In the case of a conventional combustion engine based vehicle, Indicate the driving resistance curve. Indicate lines of constant vehicle speed in case of a CVT. v = const. P e = const. T e ~ 1 ω e T e T max 5th +road inclination 4th γ = const. T e ~F t ~v 2 «driving resistance curve» T e = F r r wh γ 4 γ f T 0 ω e ω idle ω max

6 Clutch Derive two dynamic equations describing an ICE vehicle during the clutching process. v F t = T clγ i γ f r wh ω wh F a + F r + F g T cl T cl ku cl γ f γ i ω cl = v γ iγ f r wh ω e T e m v dv dt = T clγ i γ f r wh F r F a F g Θ e dω e dt = T e T cl

7 Amount of force defined by clutch pedal Use acc. pedal to balance torque und keep constant engine speed. Engine and Clutch Draw an engine map projected in the vehicle speed/traction force plane and explain what happens during a vehicle launch from standstill 1. Standstill / Idle 2. Partly releasing clutch and pressing the accelerator pedal 3. Launching vehicle with a slipping clutch 4. Accelerating with closed clutch 5. Releasing accelerator pedal to achieve fuel cut-off F t v = T max γ 1 r wh T 0 γ 1 r wh 5 Vehicle Engine v ω idle r wh γ 1 ω max r wh γ 1

8 Clutch Calculate the energy loss during takeoff of an ICE vehicle. Transfer the system dv m v dt = T clγ i γ f F r r F a F g wh dω e Θ e dt = T e T cl from its initial state v = 0, ω e = ω idle (clutch open) to the final state v = ω idler wh, ω γ i γ e = ω idle (synchronous speed) f Assume T cl = const., F r = F a = F g = 0 Then v t = T clγ i γ f t and t m v r end = r 2 wh mv wh γ 2 i γ 2 f ω idle T cl v(t) v = ω idler wh γ i γ f v = 0 t end t

9 Clutch E e = T cl ω idle t end = r 2 wh mv 2 γ 2 i γ 2 ω idle f (independent of T cl!) γ E v = T i γ f t end cl v t dt r wh 0 2 = T γ i 2 2 γ f t end cl t dt r 2 wh m v 0 2 = T γ i 2 2 γ f 2 cl ½t r 2 wh m end v = ½T cl ω idle t end = ½E e v(t) v = ω idler wh γ i γ f t end = r wh 2 mv γ i 2 γ f 2 ω idle T cl v = 0 t end t

10 Gotthard A fully loaded 28t long-haul truck should climb Gotthard (~6% slope) at 80km/h. Estimate the necessary engine displacement volume. Idea for solution: Calculate necessary traction force and power Assume engine speed -> calculate necessary engine torque Assume max mean effective pressure -> calculate necessary displacement volume. Assume stroke to bore ratio -> calculate stroke Calculate mean piston speed to verify speed assumption.

11 Gotthard A fully loaded 28t long-haul truck should climb Gotthard (~6% slope) at 80km/h. Estimate the necessary engine displacement volume. v = 80 km h 3.6 h ks 22 m s F g = m v g sin α = 16.8 kn F r = m v g cos α c r = 2.8 kn F a = 1 2 ρ ac d A f v 2 = 1 kg m m2 22 m 2 s P = v F = 22 m s 21.9 kn 480 kw 650 hp ω e = 2000 rev. rad. 200 min. s, T e P e 2400 Nm ω e V d = NπT e 4π 2400 Nm p me,max Pa m l 2.3 kn S B 3 4V d 13.6 cm c 6π e ω es π 8.2 m s (to verify speed assumption)

12 CO 2 -Emission A vehicle manufacturer claims that its 2000kg car achieves a CO 2 emission lower than 50g/km on NEDC. Double-check the claim. Idea for solution: 50g/km CO 2 can be converted into an equivalent fuel consumption in l/100km or in MJ/100km. Mechanical energy demand can be estimated by magic formula in book. The overall efficiency of the propulsion system that would be necessary to achieve

13 CO 2 -Emission A vehicle manufacturer claims that its 2000kg car achieves a CO 2 emission lower than 50g/km on NEDC. Double-check the claim. c d A f = 0.7m 2, c r = E NEDC = A f c d m v c r + 10 m v 53 m CO 2 m f = n C M CO2 M f g CO 2 g Fuel E f = V f ρ f H lhv = 1.7 η P = E NEDC E f = kg 100km 43 MJ kg g CO 2 km MJ 100km 72 % -> not achievable with an ICE! MJ 100km kg Fuel l 100 km 100km

14 Engine Generator An engine is connected to a generator. Derive the optimal operating line. Idea for solution: Assume speed-independent, torque-based Willans model for engine. Assume speed-independent, power based Willans model for generator. Express fuel consumption as function of engine torque and speed. Express fuel consumption as function of electric power and speed. Take derivative wrt engine speed to derive optimal operating line.

15 Engine Generator An engine is connected to a generator. Derive the optimal operating line. Generator: P g = P e e el P g,0, Engine: Willans. p mf = H lm f V d, where m f = P f = m f H l = p mfv d ω e Nπ m f t cycle = = p me+pme,0 V d ωe Nπe = = P e e + p me,0v d ω e Nπe = P g+p g,0 e el e = P g e el e + P g,0 e el e + p me,0v d ω e Nπe m f Nπ ω e + p me,0v d ω e Nπe TeNπ V d +pme,0 V d ωe dp f = p me,0v d > 0, but ω dω e Nπe e > ω e,idle Choose engine speed as small as possible until max torque is reached. Then go along max torque line until max power is reached. Nπe

16 Quick Check: Tram Zoo Toblerplatz Design a Flywheel to be used for storing the recuperation energy of the Züri Tram Linie 6 when descending from Zoo to Toblerplatz. Assume Tram weight = kg, and height difference = 50m E pot = mgh = kg 10 N kg 50m = 20MJ 5.5 kwh Assume rotational speed = rpm 1000 rad/s Θ f = 2E pot ω2 = 2 20MJ 2 = 40kgm 2 max rad s Assume cylinder with radius 0.25m m f = 2 Θ f = 2 40kgm2 r m2 = 1280 kg With iron of approx kg/m 3 : V = r 2 πh h = 2Θ f / ρ r 4 π 0.8m

17 Optimal Control Problem Formulate the optimal control problem for a hybrid electric vehicle. Find the control input that transfers the dynamic system x(t) = f(w(t), u t, x t ) from its initial state x(t 0 ) = x 0 to the final state x t f = x f, while respecting the state and control constraints x(t) X R n t u(t) U R m t and while minimizing the cost function J u = φ x(t f ) + t fl w t, u t, x(t) dt t 0

18 Optimal Control Problem Formulate the optimal control problem for a hybrid electric vehicle. Minimize the fuel consumption of the vehicle over a known driving cycle of length t f subject to Kinematic constraints: ω eng = ω mot = J = 0 t fmf (t) dt v t r wh γ tot,i Force/Torque/PowerBalance: T mot + T eng F tr t r wh /γ tot,i Combustion engine model: m f = f(ω eng, T eng ) Electric motor model: P b = P mot (ω mot, T mot ) Battery model: dx dt = 1 2RQ 0 U oc (x) U oc 2 (x) 4P b R b Initial/Final condition: x t f = x 0 = x 0 State constraints: x x min, x max Torque/Force/Speed Limitations

19 Dynamic Programming Derive the DP-iteration equation J k o x k = min π g N x N + = min μ k,π k+1 g x k, μ k, w k + g N x N + N 1 i=k = min μ k g x k, μ k, w k + min π k+1 g N x N + g x i, μ i, w i N 1 i=k+1 N 1 i=k+1 g x i, μ i, w i g x i, μ i, w i o J k+1 f(x k, u k, w k ) = min μ k (x k ) g x k, u k, w k o + J k+1 f(x k, u k, w k )

20 ECMS Explain how the equivalent consumption minimization strategy can be derived from Pontryagins Minimum Principle. Pontryagin tells us: u o = argmin H w, u, x o, μ o u So, if we knew the optimal value of the co-state / Lagrange multiplier / equivalence factor μ o, we could easily calculate the optimal control input u o. In case of a battery hybrid vehicle, we assume that the battery efficiency is not a function of the state-of-charge, i.e. x f u, w. Therefore μ o = x H o = μ d dx f(x, u, w) 0, and μo const. The Hamiltonian function then represents the equivalent fuel consumption : H x, u, w, μ = u + μ f x m f