pump_model_2 - CAUSAL ANALYSIS Things should be made as...

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CAUSAL ANALYSIS Things should be made as simple as possible — but no simpler. Albert Einstein How simple is "as simple as possible"? Causal assignment provides considerable insight. EXAMPLE: AQUARIUM AIR PUMP coil 60 Hz line voltage oscillatory motion in this direction magnet lever pivot flow in this direction flexible rubber bellows check valves Schematic of a low-cost aquarium air pump. • Reciprocating pump Electromagnet driven by 60 Hz line voltage Drives a small permanent magnet attached to a lever Lever drives a flexible rubber bellows on a chamber Check valves prevent flow in one direction Small flow resistance in the other Mod. Sim. Dyn. Sys. Air pump revisited page 1
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MODEL SIMPLIFICATION WAS BASED ON THREE PROPOSALS CLAIM #1 The magnet-lever-bellows combination should resonate near 60 Hz —to maximize oscillation amplitude and output flow rate CLAIM #2 Only magnet mass and bellows compliance are needed to portray resonance (other energy-storage effects are small by comparison) CLAIM #3 valve flow resistance is the only significant energy loss (other energy-dissipation effects are small by comparison) TASK: EVALUATE THESE PROPOSALS Mod. Sim. Dyn. Sys. Air pump revisited page 2
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ASSUMPTIONS Electrical sub-system AC power line — voltage source (the pump’s power load is unlikely to significantly affect line voltage) Electromagnetic coil — ideal gyrator By claims #2 & #3 all other electrical and magnetic effects are negligible. Mechanical sub-system Magnet — ideal translational inertia Its velocity is the same as that of the leftmost end of the lever — one junction Lever — ideal transformer relating two translational domains Bellows compliance — ideal translational spring (capacitor) (by claim #2) Fluid sub-system Check valves — ideal nonlinear resistors Chamber pressure proportional to bellows force — ideal transformer between translational and fluid domains Deflection of bellows compliance is the motion that pumps air — one junction Mod. Sim. Dyn. Sys. Air pump revisited page 3
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FLUID SUB-ASSEMBLY 1 10 0 0 0 R 0 R P in input from bellows Δ P Δ P out P P cham ber : : Q Q Bond graph fragment for check valves and chamber CAUSAL ANALYSIS Check valve must have flow rate output for pressure input.
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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_2 - CAUSAL ANALYSIS Things should be made as...

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