Using Bond Graph Modeling to Optimize a Mousetrap Car

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Using Bond Graph Modeling to Optimize a Mousetrap
Car

• Lester Weitman
• 4/17/2006

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Whats a Mousetrap Car?
www.docfizzix.com
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PROJECT GOALS

• Design car for 9TH grade physics project, within
  given constraints
• Standard VICTOR mousetrap
• Only spring energy _at_ 1800
• To maximize grade, car must travel
• 5 meters in under 2.75 sec
• gt 20 m total
• Physics dictates key parameters cannot improve
  both speed distance.

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MODELING GOAL

• Create BG of car and simulate speed distance w/
  varying
• Lever arm length
• Wheel diameter
• Axle diameter
• String HOOP distance to spring axis
• Wheel rotational inertia
• DIRECTIONALLY (not exactly) predictive!

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PREDICTED ISSUES RESOLVED

• Wheel friction omit (verified no slip)
• Wheel inertial mass (used I1/2M?2 for
  measured evenly distributed mass)
• Spring energy (measure actual
  mousetrap x
  .1)
  
  
• 
  

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DETERMINE PARAMETERS
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CALC Moments of Inertia
Note lumped drive wheel mass ignored smaller
undriven wheels.
Ref http//hyperphysics.phy-astr.gsu.edu/HBAS
E/icyl.htmlicyl
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CALC Spring Constant (K)

• Used sample data from DocFizzix.com to be very
  conservative
• PE ½ K Ø2
• DocFizzixs PE .8 J ? K .08 Nm/rad
• Actual Model PE 7.2 J ? K .72 Nm/rad
• DocFizzixs Initial Torque .135 Nm (used)

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CALC Spring Constant (K)

• Ref http//www.docfizzix.com/shop/tools-
  software/t100df.shtml

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CALC Spring Constant (K)

• K slope of Spring Torque vs. Angle

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CALC String Velocity
L
u
P
Ø
Law of Cosines u2L2P2-2LPcosØ
u ? x LPsinØ / sqrt(L2 P2 - 2LPcosØ) STRING
VELOCITY u
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UNANTICIPATED ISSUES

• Could not retrieve actual optimal car.
• Used 3 alternatives.
• MUCH harder to model de-bug in 20-SIM than
  anticipated!
• Had to verify kinematics were correct.
• Had to experiment to find reasonable value for
  axle friction. (Initially ignored, until
  simulation car ran forever.)

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MODELING CHALLENGES
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MODELING CHALLENGES

• Lever stops when Ø 1800
• Axle should roll freely when lever stops, so car
  continues on own momentum.
• To simplify analysis, treated car stationary
  floor moving w/ mass of car (inversing sign of
  TF at wheel).

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ISSUES RESOLVED
HALLELUJAH!
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WORKING Bond Graph Model
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WORKING Bond Graph Model
Modeled spring as MSe, setting it to ZERO when
lever stopped.
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WORKING Bond Graph Model
Modeled axle as being connected to half of axle
driven by string with a MR (rotational damper),
setting it to ZERO when lever stopped.
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CONSTANTS USED
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SAMPLE RUN Parameters
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SAMPLE RUN
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PRE-SCREENING EXPERIMENT
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SIMULATION vs. REALITY

• Directionally matched performance of actual cars.
• Matched intuition
• Longer LEVER ? string pulls longer
• Shorter P (hoop) ? string starts moving
  faster, then slows up

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Placeholder for Final
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OPTIMIZING DOE
2IV4-1 FRACTIONAL FACTORIAL DESIGN
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MiniTab Resuts Velocity
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MiniTab Resuts Distance
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NEXT STEPS

• Verify MiniTab analysis for optimized values.

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CONCLUSIONS

• 20-SIM difficult to de-bug for novice
• Need to recall tricks to simulate real world
• Attach MR
• ZERO to connect
• 999999 to disconnect
• Model only needed to be DIRECTIONALLY accurate!
• Model worked adequately in region of interest
  for optimization.

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THE END