first step bond graph hand work second step put bond graph into camp-g interface to matlab ...
TRANSCRIPT
First StepFirst StepBOND GRAPHBOND GRAPH
Hand Work
Second StepSecond Step
Put bond graph into CAMP-GPut bond graph into CAMP-G Interface to MatlabInterface to Matlab
Results: Four FilesResults: Four Files campgmod.m, campgequ.m, campgmod.m, campgequ.m,
campgnum.m, campgsym.mcampgnum.m, campgsym.m
Step ThreeStep Three
Edit campgequ.m to define:Edit campgequ.m to define: STEPSTEP EFFORTSEFFORTS TIMETIME FLOWSFLOWS
Step FourStep Four
Edit campgmod.m fileEdit campgmod.m file Input parameters:Input parameters: Initially displacement is zeroInitially displacement is zero Initially momentum is mass x velocityInitially momentum is mass x velocity
M= 1500 Kg, k1= 1 x 104 N/m,M= 1500 Kg, k1= 1 x 104 N/m, b1=500 N-s/mb1=500 N-s/m m= 100 kg, k2= 3 x 105 N/m,m= 100 kg, k2= 3 x 105 N/m, b2=8 x 104 N-s/mb2=8 x 104 N-s/m
Step FiveStep Five
Run campgmod.m file to get displacement Run campgmod.m file to get displacement and force plotsand force plots
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.2
-0.1
0
0.1
0.2 Displacement of the Car versus Time for 25 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5 Displacement of the Dummy versus Time for 25 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5000
0
5000 Force between the Dummy and Seatbelts versus Time for 25 mph
For
ce (
New
tons
)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5
0
5
10
15 Velocity of the Car versus Time for 25 mph
Vel
ocity
(m
eter
s/se
c)
Time (seconds)
Six StepSix Step
Change velocity values to see from plot if Change velocity values to see from plot if displacement of dummy is less than 1 displacement of dummy is less than 1 meter and the force is less than 6670 meter and the force is less than 6670 Newtons for one seatbeltNewtons for one seatbelt
Change velocity values to see from plot if Change velocity values to see from plot if displacement of dummy is less than 1 displacement of dummy is less than 1 meter and the force is less than 13340 meter and the force is less than 13340 Newtons for two seatbeltNewtons for two seatbelt
Seven StepSeven Step
Check hand differential equationsCheck hand differential equations Check state space form matricesCheck state space form matrices Use simulink to checkUse simulink to check
Final StepFinal Step
Design by changing bumper or seatbelt Design by changing bumper or seatbelt values for k2,b2 and k1,b1values for k2,b2 and k1,b1
Use loops to iterate for values, get max Use loops to iterate for values, get max velocity, and other factors you wantvelocity, and other factors you want
Note: See Report File for graphs and Matlab files for iterations for values
The problem states that a dummy is driving his new VW‑Rabbit into a wall! The question is to find out if his shock-absorbing bumper (k2, b2) and his seat belts (k1, b1) will prevent him from hitting the windshield without breaking his collarbone?
DATA ON INJURIES (SAE Handbook)Seat belts must be tested to 3000 lbs. (1.334 x 104) NChest can sustain a force of 1500 lbs. distributed over 30 in2.Seat belt effective area = 30 in2
Shoulder strap-seat belt combination = 60 in2
Design Criteria:1.The design for the 25 mph and 55 mph that stops the dummy from hitting the windshield is a seatbelt with the parameters of k1= 20000 N/m, b1=800 N-s/m and a bumper with the parameters of k2=100000 N/m, b2=10000 N-s/m.2.The force that is exerted on the dummy at 25 mph for one seatbelt is 4368.6 N so he is not injured internally by the seatbelt. At 55 mph the force he experiences is 9617.5 N and this is greater than the limit of 6670 N so he is crushed by the seatbelt. With the design criteria, the force at 25 mph is 2938 N and 6479.4 N at 55 mph which is below the limit of 6670 N so injuries occur. Furthermore, the force that is exerted on the dummy at 25 mph for two seatbelt is 7454.2 N so he is not injured internally by the seatbelt because the limit now is 13340 N. At 55 mph the force he experiences is 16411 N and this is greater than the limit of 13340 N so he is crushed by the seatbelt. With the design criteria, the force at 25 mph is 3701.6 N and 8171.8 N at 55 mph which is below the limit of 13340 N so injuries occur.3.The maximum velocity was determined to be 30 mph for the original parameters that allowed the dummy to be safe from the crash.4.It takes 0.1033 seconds for the dummy to hit the windshield with no seatbelts at 25 mph, 0.0714 seconds at 40 mph, and 0.0566 seconds at 55 mph. The force that is on him during the impact is zero for all the speeds.
In conclusion the best design that allowed the dummy to be safe was a seatbelt with factors k1= 20000 N/m, b1=800 N-s/m and a bumper with the parameters of k2=100000 N/m, b2=10000 N-s/m. Below is the simulink comparison which verifies the solution.
ReportReport
PHYSICAL PARAMETERSM= 1500 Kg, k1= 1 x 104 N/m, b1=500 N-s/mm= 100 kg, k2= 3 x 105 N/m, b2=8 x 104 N-s/m
SimulinkSimulinksimulinksimulinkgraphsgraphs
matlabmatlabgraphsgraphs
One SeatbeltOne Seatbelt
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.2
-0.1
0
0.1
0.2 Displacement of the Car versus Time for 25 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5 Displacement of the Dummy versus Time for 25 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5000
0
5000 Force between the Dummy and Seatbelts versus Time for 25 mph
For
ce (
New
tons
)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5
0
5
10
15 Velocity of the Car versus Time for 25 mph
Vel
ocity
(m
eter
s/se
c)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.6
-0.4
-0.2
0
0.2 Displacement of the Car versus Time for 55 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-2
-1
0
1 Displacement of the Dummy versus Time for 55 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5
1x 10
4 Force between the Dummy and Seatbelts versus Time for 55 mph
For
ce (
New
tons
)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10
0
10
20
30 Velocity of the Car versus Time for 55 mph
Vel
ocity
(m
eter
s/se
c)
Time (seconds)
Design for One SeatbeltDesign for One Seatbelt
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5 Displacement of the Car versus Time for 25 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.6
-0.4
-0.2
0
0.2 Displacement of the Dummy versus Time for 25 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-4000
-2000
0
2000
4000 Force between the Dummy and Seatbelts versus Time for 25 mph
For
ce (
New
tons
)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5
0
5
10
15 Velocity of the Car versus Time for 25 mph
Vel
ocity
(m
eter
s/se
c)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-2
-1
0
1 Displacement of the Car versus Time for 55 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5 Displacement of the Dummy versus Time for 55 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5
1x 10
4 Force between the Dummy and Seatbelts versus Time for 55 mph
For
ce (
New
tons
)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10
0
10
20
30 Velocity of the Car versus Time for 55 mph
Vel
ocity
(m
eter
s/se
c)
Time (seconds)
Two SeatbeltTwo Seatbelt
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.2
-0.15
-0.1
-0.05
0 Displacement of the Car versus Time for 25 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.6
-0.4
-0.2
0
0.2 Displacement of the Dummy versus Time for 25 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10000
-5000
0
5000 Force between the Dummy and Seatbelts versus Time for 25 mph
For
ce (
New
tons
)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5
0
5
10
15 Velocity of the Car versus Time for 25 mph
Vel
ocity
(m
eter
s/se
c)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.8
-0.6
-0.4
-0.2
0 Displacement of the Car versus Time for 55 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1.5
-1
-0.5
0
0.5 Displacement of the Dummy versus Time for 55 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-2
-1
0
1
2x 10
4 Force between the Dummy and Seatbelts versus Time for 55 mph
For
ce (
New
tons
)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10
0
10
20
30 Velocity of the Car versus Time for 55 mph
Vel
ocity
(m
eter
s/se
c)
Time (seconds)
Design for Two SeatbeltDesign for Two Seatbelt
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5 Displacement of the Car versus Time for 25 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.3
-0.2
-0.1
0
0.1 Displacement of the Dummy versus Time for 25 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-4000
-2000
0
2000
4000 Force between the Dummy and Seatbelts versus Time for 25 mph
For
ce (
New
tons
)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5
0
5
10
15 Velocity of the Car versus Time for 25 mph
Vel
ocity
(m
eter
s/se
c)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-2
-1
0
1 Displacement of the Car versus Time for 55 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.6
-0.4
-0.2
0
0.2 Displacement of the Dummy versus Time for 55 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5
1x 10
4 Force between the Dummy and Seatbelts versus Time for 55 mph
For
ce (
New
tons
)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10
0
10
20
30 Velocity of the Car versus Time for 55 mph
Vel
ocity
(m
eter
s/se
c)
Time (seconds)
Max VelocityMax Velocity
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.3
-0.2
-0.1
0
0.1 Displacement of the Car versus Time
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5 Displacement of the Dummy versus Time
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10000
-5000
0
5000 Force between the Dummy and Seatbelts versus Time
For
ce (
New
tons
)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5
0
5
10
15 Velocity of the Car versus Time
Vel
ocity
(m
eter
s/se
c)
Time (seconds)
Velocity of 30 mph
No SeatbeltsNo Seatbelts
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.2
-0.15
-0.1
-0.05
0 Displacement of the Car versus Time for 25 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-60
-40
-20
0 Displacement of the Dummy versus Time for 25 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5
1 Force between the Dummy and Seatbelts versus Time for 25 mph
For
ce (
New
tons
)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5
0
5
10
15 Velocity of the Car versus Time for 25 mph
Vel
ocity
(m
eter
s/se
c)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.4
-0.3
-0.2
-0.1
0 Displacement of the Car versus Time for 40 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-100
-50
0 Displacement of the Dummy versus Time for 40 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5
1 Force between the Dummy and Seatbelts versus Time for 40 mph
For
ce (
New
tons
)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10
0
10
20 Velocity of the Car versus Time for 40 mph
Vel
ocity
(m
eter
s/se
c)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.8
-0.6
-0.4
-0.2
0 Displacement of the Car versus Time for 55 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-150
-100
-50
0 Displacement of the Dummy versus Time for 55 mph
Dis
plac
emen
t (m
eter
s)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5
1 Force between the Dummy and Seatbelts versus Time for 55 mph
For
ce (
New
tons
)
Time (seconds)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10
0
10
20
30 Velocity of the Car versus Time for 55 mph
Vel
ocity
(m
eter
s/se
c)Time (seconds)
Excel Numbers