pump_model_1 - MULTI-DOMAIN MODELING WHAT'S THE ISSUE? Why...

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Unformatted text preview: MULTI-DOMAIN MODELING WHAT'S THE ISSUE? Why not just “write down the equations”? — standard formulations in different domains are often incompatible usually due to incompatible boundary conditions (choice of “inputs”) EXAMPLE: SIMPLE FLUID SYSTEM Scenario Modeling goal The simplest model competent to portray resonance in this system. Assumptions • rigid-body motion (e.g., lever & pivot do not bend) • mass concentrated at c.g. of magnet • electro-magnet applies an oscillating force • small motion • mechanical elasticity only in the flexible bellows • no power dissipation except in the check valves (this assumption highlights any resonant behavior) • linear model of mechanical-to-fluid transduction • incompressible fluid • ideal check valves “Write down” the equations First define quantities: l 1 l 2 y 1 y 2 m P lef t P chamber P right A k Modeling and Simulation of Dynamic Systems Air pump model page 2 Mechanical Domain m ÿ 2 := F magnet – F spring – F dissipation (symbol := denotes an assignment operator; right side is computed to evaluate left side.) F spring := k l 1 l 2 y 2 F dissipation is due to fluid forces. Substituting: m ÿ 2 := F magnet – l 1 l 2 k l 1 l 2 y 2 – l 1 l 2 F dissipation This implies state equations:...
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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.

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pump_model_1 - MULTI-DOMAIN MODELING WHAT'S THE ISSUE? Why...

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