Problem 6.1. For a single cylinder internal combustion engine with schematic diagram shown in Figure P6.1:

Size: px

Start display at page:

Download "Problem 6.1. For a single cylinder internal combustion engine with schematic diagram shown in Figure P6.1:"

Elaine Bond
6 years ago
Views:

1 Proble 6. For a single cylinder internal cobustion engine with scheatic diagra shown in Figure P6.: a. Explain clearly how any transforers, gyrators, inertia eleents, capacitor eleents and resistor eleents do you find in the bond graph? b. Construct the coplete bond graph, nuber it and insert the causal strokes. c. Specify the state variables of the syste. A P, Q K r l Figure P6. Scheatic diagra of engine for Proble 6. C: k P Q A F v n T M T e e Figure S6 ond graph of Proble 6.

2 C A 6 3 n M Figure S6 Nubering and causal strokes for the ond graph of Proble 6. Proble 6. For a cylinder internal cobustion engine with scheatic diagra shown in Figure P6.: a) Construct the bond graph. b) Assign the causal strokes and specify the state variables. P,Q P,Q K K r l Figure P6. Scheatic diagra of engine for Proble 6.

3 7 3 C 9 7 M M C Figure S6. ond graph of Proble 6. Proble 6.3 For a cylinder internal cobustion engine with scheatic diagra shown in Figure P6.3: a) Construct the bond graph b) Assign causal strokes and specify the state variables. P,Q P,Q P,Q P,Q 3 3 K K K 3 K r l Figure P6.3 Scheatic diagra of engine for Proble 6.3

4 C 7 M M 7 C C M M C Figure S6.3 ond graph of Proble 6.3 Proble 6. Consider a speed constant esh gearbox shown in Figure P6.: a) Construct bond graph for the syste when gear is engaged. b) nsert causal strokes and then specify the state variables. c) What changes will occur to the bond graph when another gear is engaged? Explain why? N, o o N i, i i 3 K o nput shaft K i L i o Layshaft Output shaft N L, L K L K L N, N,

5 Figure P6. Scheatic diagra of gearbox for Proble 6. C i C L C L C o i L eq eq + eq3 + eq + eq T i i N L /N i N o /N T o o i L o Figure S6.. ond graph of Proble 6. T S i e i 6 C i i L 6 9 N L /N i N o /N 7 9 T o i 3 L 3 C L eq C L eq + eq3 + eq + eq 9 o 7 o C o Figure S6.. Nubering and causal strokes for bond graph of Proble 6. Proble 6. For a vehicle differential with details shown in Figure P6.: a) Draw a coplete bond graph. b) Assign proper causal strokes. c) Specify the appropriate state variables.

6 p T p N P, P N C, C 3 L T L T N 3, 3 N,, Figure P6. Scheatic diagra of differential for Proble 6. P T p p nf C T T / C F F L F T / C F F L F T L L Figure S6.. ond graph of Proble 6.

7 F A F L F Figure S6.. Free-body-diagra of idler gear P T p p nf C T T / C F F L F T / C F F L F T L L Figure S6..3 Causally stroked bond graph Proble 6.6 For the planetary gear set shown in Figure P6.6 construct the bond graph for following cases: a) When the Carrier C is fixed ( T input and TS output) b) When the Sun S is fixed ( T input and TC output) c) When the ing is fixed ( T S input and TC output)

8 d) Write the equations of otion of syste in case (a) ing gear, Sun gear, S Planet gear, P T C T S S C T O S C P Planet carrier, C Figure P6.6 Scheatic diagra of epicyclic gear set for Proble 6.6 F F C F F S F C P S T S T C C F S T Figure S6.6. Free-body-diagras of planetary gear coponents P S T P/ - S/ P T S S Figure S6.6. ond graph of Proble 6.6, part (a)

9 P P C T P/ / P F C v C C T C C Figure S6.6.3 ond graph of Proble 6.6, part (b) S P P C T S S P/ S / P F C v C C T C C Figure S6.6. ond graph of Proble 6.6, part (c) P S 3 T P/ - S/ P 6 7 T S S Figure S6.6. Nubering and stroke of bond graph of Proble 6.6, part (a) Proble 6.7 A rigid body odel of the driveline is represented as a siplified odel in Figure P6.7 by ignoring daping. a) Derive the equations of otion of the syste (note the differential causalities). b) Find the equation for the angular acceleration W of the wheel c) Find an expression for the overall gear ratio n that axiizes W d) s the result useful?

10 EQ W T e e n /r W v W Figure P6.7 igid body bond graph odel of Proble 6.7 EQ W n 3 6 /r W 7 v W Figure S6.7 Causal strokes for the ond graph of Proble 6.7 Proble 6. epeat Exaples 6.., 6.. and 6..3 for an initial speed of /s and gear ratio of.

11 Vehicle acceleration (/s) Vehicle speed (/s) Clutch spring torsion (degree) Engine speed (rp) Figure S6.. Engine speed and clutch spring torsion of Proble 6. for clutch copliance Figure S6.. Vehicle speed and acceleration of Proble 6. for clutch copliance

12 Vehicle acceleration (/s) Vehicle speed (/s) Driveshaft torsion angle (degree) Engine speed (rp) Figure S6..3 Engine speed and clutch spring torsion of Proble 6. for driveshaft copliance Figure S6.. Vehicle speed and acceleration of Proble 6. for driveshaft copliance

13 Driveshaft rotation angle (degree) Clutch rotation angle (degree) Driveshaft speed (rp) Engine speed (rp) Figure S6.. Engine and driveshaft speed of Proble 6. for cobined clutch and driveshaft copliances

14 vehicle acceleration (/s) vehicle speed (/s) Figure S6..6 Clutch spring and driveshaft torsion of Proble 6. for cobined clutch and driveshaft copliances Figure S6..7 Vehicle speed and acceleration of Proble 6. for cobined clutch and driveshaft Proble 6.9 copliances epeat Exaples 6.., 6.. and 6..3 for an initial speed of /s and a sudden release of accelerator pedal. n this case the engine will generate a braking torque that can be odelled by the relation Tbe. ( e in rad/s). e

15 Vehicle acceleration (/s) Vehicle speed (/s) Clutch spring torsion (degree) Engine speed (rp) Figure S6.9. Engine speed and clutch spring torsion of Proble 6.9 for clutch copliance Figure S6.9. Vehicle speed and acceleration of Proble 6.9 for clutch copliance

16 Vehicle acceleration (/s) Vehicle speed (/s) Driveshaft torsion angle (degree) Engine speed (rp) Figure S6.9.3 Engine speed and clutch spring torsion of Proble 6.9 for driveshaft copliance Figure S6.9. Vehicle speed and acceleration of Proble 6.9 for driveshaft copliance

17 Driveshaft rotation angle (degree) Clutch rotation angle (degree) Driveshaft speed (rp) Engine speed (rp) Figure S6.9. Engine and driveshaft speed of Proble 6.9 for cobined clutch and driveshaft copliances Figure S6.9.6 Clutch spring and driveshaft torsion of Proble 6.9 for cobined clutch and driveshaft copliances

18 vehicle acceleration (/s) vehicle speed (/s) Figure S6.9.7 Vehicle speed and acceleration of Proble 6.9 for cobined clutch and driveshaft copliances Proble 6. epeat Proble 6.9 for an initial speed of /s and gear ratio of.

19 Vehicle acceleration (/s) Vehicle speed (/s) Clutch spring torsion (degree) Engine speed (rp) Figure S6 Engine speed and clutch spring torsion of Proble 6. for clutch copliance Figure S6 Vehicle speed and acceleration of Proble 6. for clutch copliance

20 Vehicle acceleration (/s) Vehicle speed (/s) Driveshaft torsion angle (degree) Engine speed (rp) Figure S63 Engine speed and clutch spring torsion of Proble 6. for driveshaft copliance Figure S6 Vehicle speed and acceleration of Proble 6. for driveshaft copliance

21 Driveshaft rotation angle (degree) Clutch rotation angle (degree) Driveshaft speed (rp) Engine speed (rp) Figure S6 Engine and driveshaft speed of Proble 6. for cobined clutch and driveshaft copliances Figure S66 Clutch spring and driveshaft torsion of Proble 6. for cobined clutch and driveshaft copliances

22 Throttle (%) vehicle acceleration (/s) vehicle speed (/s) Figure S67 Vehicle speed and acceleration of Proble 6. for cobined clutch and driveshaft copliances Proble 6. epeat Exaples 6.., 6.. and 6..3 for a 3 second pulse of throttle shown in Figure P6 Use the braking torque of Proble 6.9. t (s) Figure P6. Throttle pulse of Proble 6.

23 Vehicle acceleration (/s) Vehicle speed (/s) Clutch spring torsion (degree) Engine speed (rp) Figure S6 Engine speed and clutch spring torsion of Proble 6. for clutch copliance Figure S6 Vehicle speed and acceleration of Proble 6. for clutch copliance

24 Vehicle acceleration (/s) Vehicle speed (/s) Driveshaft torsion angle (degree) Engine speed (rp) Figure S63 Engine speed and clutch spring torsion of Proble 6. for driveshaft copliance Figure S6 Vehicle speed and acceleration of Proble 6. for driveshaft copliance

25 Driveshaft rotation angle (degree) Clutch rotation angle (degree) Driveshaft speed (rp) Engine speed (rp) Figure S6 Engine and driveshaft speed of Proble 6. for cobined clutch and driveshaft copliances Figure S66 Clutch spring and driveshaft torsion of Proble 6. for cobined clutch and driveshaft copliances

26 vehicle acceleration (/s) vehicle speed (/s) Figure S67 Vehicle speed and acceleration of Proble 6. for cobined clutch and driveshaft copliances Proble 6. Consider the bond graph of whole vehicle for straight ahead otion and ignore propeller shaft elasticity and: a) Siplify it by cobining the eleents around the iddle transforers. b) nsert causal stokes and specify the state variables of syste. c) Derive the equations of otion of the resulting bond graph.

27 cv C c e c g p T e e n g M n f e cd g p sv C s t C t cw+ d s+ w v /r W F v d s Figure S6.. Straight-ahead bond graph of driveline after ignoring propeller elasticity c g p cw+ d eq n g M n f n M g p d eq Figure S6.. Cobination of two transforers T e e cv e 6 7 C c sv C s t C t n M eq s+ w /r W v 3 e cd eq s v Figure S6..3 The bond graph of equivalent syste with causal strokes

28 Proble 6.3 Consider the bond graph of whole vehicle for straight-ahead otion and: a) Siplify it by cobining the eleents around the transforers. b) For (a) insert causal strokes and specify the state variables of syste c) Derive the equations of otion of syste. cv e C c pv E C p T e e 3 n g 3 6 M n f e cd g sv E 7 3 C s t C t 6 s+ w /r W v v E s Figure S6.3 The bond graph of equivalent syste with causal strokes Proble 6. Consider the rigid-body odel of driveline. a) Copare the syste of Proble 6.7 with the rigid-body odel and deterine W and EQ. b) Specify which coponents have been ignored. c) Describe what the syste of Proble 6.7 is telling you and if it is coparable to what was discussed in Chapter 3.

29 e+ c g+ p cw+ d+ s W v T e e n g M n f /r W a e g+ p d+ s W Figure S6.. Modified bond graph of rigid body driveline EQ W v T e e n /r W a EQ W Figure S6.. Siplified bond graph of rigid body driveline

JJMIE Jordan Journal of Mechanical and Industrial Engineering

JJMIE Jordan Journal of Mechanical and Industrial Engineering Volue, Nuber 3,Sep. 008 ISSN 995-6665 Pages 57-6 Matheatical Modeling for Pup Controlled Syste of Hydraulic Drive Unit of Single Bucket Excavator