bond_graph_primi

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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! ...
View Full Document

This note was uploaded on 02/27/2012 for the course MECHANICAL 2.141 taught by Professor Nevillehogan during the Fall '06 term at MIT.

Ask a homework question - tutors are online