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bond_graph_primi

# bond_graph_primi - T h e Basic Bond Graph Primitives...

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Unformatted text preview: T h e Basic Bond Graph Primitives Fundamental quantities and relations P : p o w e r e: effort p: m o m e n t u m e = f: flow dpldt dq/dt Denotes E : energy q: displacement f Bond Graph Symbol = Electrical Network Icon Typical M echanical Icon power port or bond o p t i o ~variable labels l e energetic interaction between im p licit im p l i c i t half arrow denotes direction ofpositive powerflow (sub)system s (generalized) capacitor Ceffort = electrical capacitor (generalized) potential m echanical spring @(displacem ent) energy storage volts = @(charge) force = @(displacement) ideal, linear capacitor: ideal, linear spring: e potential energy = E,(displacem ent) E, = = q/C q2/2c F = k x Bond Graph Symbol Denotes Electrical Network Icon Typical M echanical Icon (generalized) inertia Iflow = electrical inductor (generalized) potential energy translational inertia '%'(momentum) storage current = '%'(flux l i n k a g e ) velocity = y(m om entum) ideal. linear inductor: ideal, linear spring: kinetic energy = Ek(mom entum) (generalized) dissipator irreversible Reffort = electrical resistor energy removal viscous dam per r(f1ow) volts = r(current) force = T(ve1ocity) inverse m a y also be definable ideal, linear resistor: ideal, linear damper: e = R i Bond Graph Symbol Denotes Electrical Network Icon Typical M echanical Icon effort source boundary condition o p t i o n a t futt a r r o w d e n o t e s modulating signal voltage source force source specifying effort (no consensus) flow source boundary condition o p t i o n a l full a r r o w d e n o t e s modulating signal current source velocity source specifying flow (no consensus) Bond Graph Symbol Denotes com m on effort connection e 1 = e1 ' v i , j . . continuity equation Electrical Network Icon Typical M echanical Icon zero junction n u m b e r o f p o r t s is u n r e s t r i c t e d parallel connection n e t p o w e r in is z e r o : Coieifi i = Coifi i = 0 o im p l i c i t in d i a g r a m ambiguous bi 1 if half-anowinwards, -1 if half-armw outwards = one junction n u m b e r o f p o r t s is u n r e s t r i c t e d com m on flow connection series connection i m p l i c i t in d i a g r a m ambiguous com patability equation n e t p o w e r in is z e r o : Bond Graph Symbol Electrical Network Icon Typical M echanical Icon transformer powercontinuous energy el f2 = = electrical transform er m echanical lever T e2 T fl = transduction p o w e r in elfl = power out e2f2 gyrator powercontinuous energy e2 el = = G fl G f2 = transduction p o w e r in elfl = power out e2f2 Ambiguity of Series and Parallel for M echanical System s E l e c t r i c a l e l e m e n t s in p a r a l l e l h a v e t h e s a m e v o l t a g e . E l e c t r i c a l e l e m e n t s in s e r i e s h a v e t h e s a m e c u r r e n t . A : These t w o springs are a p p a r e n t l y in parallel. T h o u g h A & B are visually d i f f e r e n t , in b o t h c a s e s knowing the displacement of one spring determines the displacement of the other. B : These two springs are , ' + + A / a p p a r e n t l y in s e r i e s . // / + / T h o u g h A & C are visually similar, the relation b e t w e e n spring d i s p l a c e m e n t s is d i f f e r e n t : in C t h e displacements are independent. T h o u g h B & D are visually sim ilar, the relation between spring d i s p l a c e m e n t s is d i f f e r e n t : in D t h e displacements are independent. T h o u g h C & D are visually d i f f e r e n t , in b o t h c a s e s t h e displacement of o n e spring is i n d e p e n d e n t o f the other. C : These two springs are a p p a r e n t l y in p a r a l l e l . D : These two springs a r e a p p a r e n t l y in s e r i e s . S o m e Bond Graph Embellishments Parameters of ideal linear elem ents m ay be written adjacent to the element symbol. Ilk :C L :I - ideal, linear m echanical spring ideal, linear electrical inductor Their com m on variables m ay b e written a d j a c e n t to z e r o - o r o n e - junctions. Variables of source elements m a y b e written a d j a c e n t to the element symbol. mechanical velocity A line with a full arrow head m a y denote "signal" transmission (without power exchange). -bSf / source USE SPARINGLY AND CAREFULLY! ...
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