Transcript Document

Using Bond Graph Modeling to
Optimize a Mousetrap Car
Lester Weitman
4/17/2006
7/21/2015
1
What’s a Mousetrap Car?
www.docfizzix.com
PROJECT GOALS:

Design car for 9TH grade physics project,
within given constraints:
– Standard VICTOR® mousetrap
– Only spring energy @ 1800

To maximize grade, car must travel:
– 5 meters in under 2.75 sec; &
– > 20 m total

Physics dictates key parameters cannot
improve both speed & distance.
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!
PREDICTED ISSUES RESOLVED:
• Wheel friction: omit
(verified no slip)
• Wheel inertial mass:
(used I=1/2Mω2 for
measured evenly distributed mass)
• Spring energy:
(measure actual
mousetrap x .1)
DETERMINE
PARAMETERS
CALC: Moments of Inertia
A solid cylinder of
mass m=
.03
kg
10
and radius R =
cm
will have a moment of inertia about its central axis:
Icentral axis =
0.0001
kg m2
Note: lumped drive wheel mass & ignored smaller undriven wheels.
Ref:
http://hyperphysics.phy-astr.gsu.edu/HBASE/icyl.html#icyl
CALC: Spring Constant (K)

Used sample data from DocFizzix.com
to be very conservative:
– PE = ½ K Ø2
– DocFizzix’s PE = .8 J
 K= .08 Nm/rad
– Actual Model PE = 7.2 J  K= .72 Nm/rad
– DocFizzix’s Initial Torque = .135 Nm
(used)
CALC: Spring Constant (K)
Lab #2 All Wound Up
Data was collected by measuring force per angle with a force probe and a torsion wheel. Record the
radius of the torsion wheel, or the length of the measuring arm in (D12) and record the force as well as
angle in (C22-C?) and (B22-B?)
BLUE ITEMS - Data that is measured and entered from experimen. DO NOT CHANGE BLACK NUMBERS
Spring to drive axle =
0.18
Measure the distance from the center of the mousetrap's spring to the drive axle
Actual lever arm length =
0.18
Measure the length of the leverarm
Testing Arm Length (m) =
0.05875
Total Starting Potential Energy (J) =
NOTE: If you are using Doc Fizzix's Torsion Wheel DO NOT change this value
0.8107
Spring Constant - Based on slope of Torque vs. Angle (Nm/rad) =
0.0795
Spring Constant - Based on average of all Spring Constants (Nm/rad) =
0.0778

Ref:
http://www.docfizzix.com/shop/tools- software/t100df.shtml
CALC: Spring Constant (K)
K
= slope of Spring Torque vs. Angle
CALC: String Velocity
L
u
P
Ø
Law of Cosines: u2=L2+P2-2LPcosØ
ů= ω x LPsinØ / sqrt(L2 + P2 - 2LPcosØ)
STRING VELOCITY = ů
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.)

MODELING CHALLENGES:
1
2
3
Lumped mass of car
MODELING CHALLENGES:
1.
Lever stops when Ø = 1800
2.
Axle should roll freely when lever stops,
so car continues on own momentum.
3.
To simplify analysis, treated car
stationary & floor moving w/ mass of
car (inversing sign of TF at wheel).
ISSUES RESOLVED:
HALLELUJAH!
WORKING Bond Graph Model:
WORKING Bond Graph Model:
Modeled spring as MSe, setting it to ZERO when lever stopped.
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.
CONSTANTS USED:
SAMPLE RUN: Parameters
SAMPLE RUN:
PRE-SCREENING EXPERIMENT:
RUN
1
2
3
4
5
6
7
L
.1
.1
.2
.08
.08
.08
.08
P
.1
.1
.2
.08
.08
.04
.04
Rw
.05
.05
.05
.05
.08
.08
.08
Ra
.002
.002
.002
.002
.002
.002
.004
DISTANCE
22
24
22.7
20
46
45
45
5m in x s
3.18
3.69
4.5
2.9
3.4
1.9
1.6
Jw
.0000125
.0000125
.00000125
.00000125
.00000125
.00000125
.00056
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
Placeholder for Final
OPTIMIZING DOE:
2IV4-1 FRACTIONAL FACTORIAL DESIGN
RUN
1
2
3
4
5
6
7
8
L
.08
.2
.08
.2
.08
.2
.08
.2
P
.04
.04
.2
.2
.04
.04
.2
.2
Rw
.05
.05
.05
.05
.1
.1
.1
.1
Ra
.002
.006
.006
.002
.006
.002
.002
.006
DISTANCE
18.7
18.4
18.6
22.8
72
73
74
55
5m in x s
1.8
1.6
1.7
4.5
1.6
1.8
2.4
3.3
MiniTab Resuts:
Velocity
Pareto Chart of the Effects
(response is VEL, Alpha = .10)
A:
B:
C:
D:
B
AB
A
D
AC
C
AD
0.0
0.5
1.0
L
P
Rw
Ra
MiniTab Resuts:
Distance
NEXT STEPS:

Verify MiniTab analysis for optimized
values.
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”.

THE
END