lecture 2 - FUNDAMENTALS OF BOND GRAPH'MODELING METHOD...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: FUNDAMENTALS OF BOND GRAPH'MODELING METHOD Conservation of Energy is key (note power and energy are scalar quantities): 6E ZPinJ = :3? + ZPouLj Net power into system=rate of change of energy in systeniLI-net power out of system Define Power Conjugates variables: Translation F, force V, velocity Rotation 1, torque (2 , angular velocity ' Fluid/Hydraulic P, pressure Q, flow rate Electrical _ e, voltage i, current H Thermal T, temperature €— , time-rate of change of entropy, s t g «in .- Flow-Effort variables (developed by James C. Maxwell) Effort variables “e”: ‘pushing’: F, T, P, e, T - . . ds ' F1 b1 :”’:‘ t ’2V9 '— ow varia es f mo 10n , ,Q, 1, dt I. Power, P=ef It Energy, E= I}.ng = J'efdt Define energy variables: Generalized momentum: p = Jedt Generalized displacement: q = det Energy of a system can be rewritten as: E = Ifdp “kinetic” energy E = jedq “potential” energy we: m5 BOND GRAPHS Bond graph modeling elements: 0 Energy storage elements (C, I) 0 Energy dissipation elements (unavailable forms) (R) 0 Energy transforming elements (T, G) '0 Junction structures (1, 0) ‘ 0 Power sources and sinks (Se, Sf) Port: place at which power can be exchanged For example: at sources/sinks, energy storage elements, Ports are represented by short line segments: effort is written above or to the lefi of the line, while flow is written below or to the right of the line. Half arrows on the segments point in the direction of positive power flow. For C and I elements, power can flow in or out, so the half arrows can point in either direction. R elements always remove power, so the half arrow is always directed toward R. ’ Se and Sf : Sources supply power to a system and the half arrow points away from the source and toward the system. Sinks drain power from a system and the half arrow points toward the sink and away from the system. Junctions are used to connect the basic elements together. 0 junction: common effort-every port connected to it has the same effort 2 fl. = O Flows divide (Kirchoffs Current Law) [:1 1 junction: common flow: every port connected to it has the same flow m 2 el. = 0 Efforts divide (Kirchoffs Voltage Law) [:1 TABLE 3‘4 M Bond Graph Symbol Defining Relation Generalized variables 54.— 8(1) givcn‘ f (I) arbitrary Sf—a fm given. w) arbitrary Mechanical translation Sf—“ Hz) given, 31(1) arbitrary Sv—fi VU} given. Fm arbitrary Mechanical rotan'on St #- rm gwcn. mm arbitrary Sm~ mm given, 1(1) arbitrary Hydraulic systems 5p~ PU) given, Qtr} arbitrary SQ- Qm given, PU) arbitrary Electrical systems Se ~ e (t) given, i (t V) arbitrary 5, ~ in) given. 90) arbitrary One Port Elements F P ..__.A.e “R ._._AR 1. R V Q (c) FIGURE 3.1. The i—purt resistor. (43) Bond graph symbol; ([2) defining relation; (6) represen- anions in several physical domains. TABLE 3.1. The 1-Port Resistor, i R I General Linear SI Units for Linear Relation Relation Resistance Parameter Generalized variables e 2- (hmf) e = Rf R = e/f fxcbglie) fnGe=efR Mechanical translation F = (bf V) F = IN 27 = N-s/m v = Cb“ (F) Mechanical rotation r = d>(w') r = cm 6 :2 N-m—s a) = d)" (r) Hydraulic systems P = @(Q‘) P = RQ R = N-s/mS Q = v” (P) Electrical systems 8 :2 $0“) 0 n Rz’ R = VIA = 9 (ohm) i=d>"1(e) i=Ge l» P 9:21-132 P r l 2 L Q Q~X~>Q : I .37“! Q I 7w FIGURE 3.4. The l-pon inertia. (a) Bond graph symbol; (1‘)) defining relation; (6‘) mprcsen- union in several physical domains. TABLE 3.3. The 1-Port Inertia, ‘3‘? I I General Linear SI Units for Linear Relation Rcia’mm lnertance Paramemr Generaiizcd p = dang”) p m 1f 1 = pf'f vafiabies f = dfi’gp) - r. pg; 1,; a 3, Mechanical p = d), (v; p s m v m = N-szlm translation v 2 my‘ip) v :2 pm Mechanical pt = (Dim) p, x M; J := N-m~52 rotation w=¢flipd w==PEH Hydraulic p,, = «mg; pp = IQ I .~. Nuszlm5 systems Q = mrln'pp) Q = pw metrical A = mm} .3. = Li L = v.5/A systems 1‘ z a); 1 (A) i 2 UL = bemys (H) q 3: QC (9’ e a: 65%) e MC f q Ef fit (a) (5} 1' V, = X FP— X », 1g T1 r i E F P e «cum—H ..._, - $.3— IQ e F P M wan—uh. M I. C v. C Q C Air 9, 92 biadder .3... “L. Q s a 01 ~— 02 T w 3 6 .P M—fi , P ._.—.AC C a: Q (C) FIGURE 3.2. The 1-port capacitor. (3} Bond graph symbol; ([7) defining relation; (C) repre- sentation in several physmai domains. TABLE 3.2. The 1.13m Cayacitor. i c ' f=é Genera} Linear SI Units for Linear Relation Relation Capacitance Parameter Generalized q = was) .9 = Ce C = qj‘e e=¢Ez¢IqJ ezq/C lx‘Czefq Mechanical X m (bfhr) X :z: C = min translation F = ¢g‘(X; F = kX k m N/m Mechanical 9 : (bar) 9 2 Cr C :: mdi~m rotation 1' = «>31 (8) z 2 k9 k z: N«m/rad Hydraulic v = chap) 1» -.-.~ cp c = {HS/N systems P m 455’ (V) P = WC Electrical q : (Dds) q :: Ce C : A‘s/V systcms e = Q35] (q) e = q/‘C == farm (F)- 3 ' ‘ ‘1’. \/‘~'" \ ’ - F \ _ . ,.—«~—~\__._.\_.. _J_ 113.. . f) T 37502 Q\ Q2 "7) of f} f2 Wax/157‘ W 8’ Zméz ) m7} :f2 ‘8! g: fl 7": 7? f9 W W cauaww‘m TWO Port Elements 8} 32 .._._.....__.n TF -————-. f1 {2 (a) (d) FIGURE 3.8. Transfenners. (a) Bond graph; {in} ideal rigid lever; (6') gear pair: (d) elecmcal transformer; is) hydrauhc ram. FIGURE 3.9. Gyrators. (a) Bond graph; (b) symbol for electrical gymtor; (cf; machanical gymtor; (d) voice coil transducer. €1$rfz rfiZQ’Z- Three Port Elements ‘13 .40“. I 2 “E3 jihad“ =i=y =V Hm V1 V2 V3 FIGURE 3.1]. Basic 31mm in various physical domains. {a} @jnnction; (b) l-juncu'on. TABLE 3.5. Summary of Bagic 3—Ports f} 8‘ How junctianfi I “*7 ()_ 7 e; z 62 x 83. or (Ir-junction “"3 f1 + 154* f3 = D . . E ,. .- Effortjuncuon. M I f1 = f: = $3. . . a w W, or lajuncuon ' UL 1“ e; 4» 9» + as = O ...
View Full Document

This document was uploaded on 04/02/2012.

Page1 / 12

lecture 2 - FUNDAMENTALS OF BOND GRAPH'MODELING METHOD...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online