Transcript Rockets - Harvey Mudd College

Rocket Flight Dynamics
Section 1, Team 4
Student 1, Student 2, Student 3
May 5, 2008
Rockets Analyzed
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Large IMU rocket
Large vibration rocket
Small vibration rocket
All launches at Lucerne Valley dry lake bed
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Altitude: 2848 feet
How the RDAS functions
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6 channels of data
Onboard accelerometer
Onboard pressure sensor
Samples at 200 Hz
Runs on 9V battery supply
IMU and Vibration Sensors
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IMU
3 MEMS Accelerometers
• 3 MEMS Gyroscopes
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Vibration
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Piezoelectric strain gauges
X axis
Z axis
Y axis
Modal Shapes
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Model rocket as a uniform beam
At natural frequencies, distinct modal shapes
Values of natural frequencies depend on beam
dimensions and material properties
Mode 1:
Mode 2:
Mode 3:
.
Large IMU Rocket
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Launched April 26, 2008 with G339N motor
RockSim used to model launch
Estimated Apogee of 482.66 ft
Large IMU Rocket
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Approximations
Any point before time=0 needs to be set to zero
• Account for calibration drift
• Over thrust curve, all other sensors should be zero
• Noisy x and z gyroscopes have negligible effect
• Integration error doesn’t affect apogee
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Y position (feet)
Altitude (feet)
Apogee at 5.45 seconds
• Made several
approximations to
eliminate noise
• Model only works until
apogee
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X position (feet)
Large IMU Rocket
Flight Path Model for Large IMU Flight 4 (no rotation)
100
X: 5.45
Y: 106.1
50
0
0
1
2
3
Time (sec)
4
100
5
6
X: 5.45
Y: 115.5
50
0
0
1
2
3
Time (sec)
4
400
5
6
X: 5.45
Y: 490.2
200
0
0
1
2
3
4
Time (sec)
5
6
Large Vibration Rocket
Launched April 19, 2008 with G69N motor
• Severe weathercock
• RockSim trajectory portrays weathercock
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Large Vibration Rocket
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Six vibration sensors connected to RDAS
Sensor 10 assumed as input
3
5
72.39cm
ADC0
60.64cm
ADC1
6
7
46.67cm 31.75cm
ADC2
ADC3
8
10
15.875 cm
ADC4
0 cm
ADC5
Large Vibration Rocket
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Applied Fourier transform
Treating sensor 10 as input, plotted FRF
5
6
x 10
Sensor 3 Frequency Response
Sensor 5 Frequency Response
1500
4
1000
2
500
0
-100
-50
0
50
Sensor 6 Frequency Response
100
60
0
-100
4
x 10
4
-50
0
50
Sensor 7 Frequency Response
100
-50
0
50
Sensor 10 Frequency Response
100
40
2
20
0
-100
-50
0
50
Sensor 8 Frequency Response
100
600
0
-100
2
400
1
200
0
-100
-50
0
50
100
0
-100
-50
0
50
100
Large Vibration Rocket
Identified three resonant peaks
• Mode 1 assumed to be at 23.85 Hz
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Modal Shape at 23.85 Hz
0.1000
0.0000
0
10
20
30
40
-0.1000
Magnitude
-0.2000
-0.3000
-0.4000
-0.5000
-0.6000
-0.7000
-0.8000
Position from motor (cm)
50
60
70
80
Large Vibration Rocket
Mode 2 assumed to be at 0.9569 Hz
Modal Shape at 0.9569Hz
1.0000
0.5000
0.0000
0
10
20
30
40
-0.5000
Magnitude
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-1.0000
-1.5000
-2.0000
-2.5000
-3.0000
-3.5000
Position (cm)
50
60
70
80
Large Vibration Rocket
Higher Mode at 19.65 Hz
Modal Frequency at 19.65 Hz
1.2000
1.0000
0.8000
Magnitude
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0.6000
0.4000
0.2000
0.0000
0
10
20
30
40
-0.2000
Position (cm)
50
60
70
80
Small Vibration Rocket
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Launched April 19, 2008 with G104T motor
Camera drew power from battery
Parachute did not deploy
Small Vibration Rocket
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Five vibration sensors connected to RDAS
Sensor 10 chosen as input
1
5
37 in
ADC0
6
28 in
ADC1
8
22 in
ADC2
10
8 in
ADC4
1 in
ADC3
Small Vibration Rocket
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Applied Fourier transform and 50 Hz filter
Treating sensor 10 as input, plotted FRF
4
8
x 10
Sensor 1 Frequency Response
Sensor 5 Frequency Response
6000
6
4000
4
2000
2
0
-100
-50
0
50
100
0
-100
Sensor 6 Frequency Response
4000
2
3000
1.5
2000
1
1000
0.5
0
-100
-50
4
2
x 10
0
50
100
Sensor 8 Frequency Response
1.5
1
0.5
0
-100
-50
0
50
-50
0
50
100
Sensor 10 Frequency Response
100
0
-100
-50
0
50
100
Small Vibration Rocket
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Identified two resonant frequency peaks
Mode 1 assumed to be at 7.997 Hz
Modal Shape at 7.997 Hz
0.4000
0.2000
0.0000
-0.2000
Magnitude
•
0
5
10
15
20
-0.4000
-0.6000
-0.8000
-1.0000
-1.2000
-1.4000
Position (in)
25
30
35
40
Small Vibration Rocket
Mode 2 assumed to be at 0.5831 Hz
Modal Shape at 0.5831 Hz
9.0000
8.0000
7.0000
6.0000
Magnitude
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5.0000
4.0000
3.0000
2.0000
1.0000
0.0000
-1.0000 0
5
10
15
20
Position (in)
25
30
35
40
Summary
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Large IMU
Apogee at 5.45 seconds
• Modeled altitude at apogee of 3382 feet
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Large Vibration
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Three natural frequencies: 23.85 Hz, 0.956 Hz,
19.65 Hz
Small Vibration
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Two natural frequencies: 7.997 Hz, 0.5831 Hz
Acknowledgements
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E80 lab professors
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Mary Cardenas, Reza Miraghaie, Erik Spjut, Ruye
Wang, and Qimin Yang
Lab proctors and Rocket Development Team
Reference 1
Reference 2
Reference 3
References
Miraghaie, Reza, Modal Vibration,
http://www.eng.hmc.edu/NewE80/PDFs/ModalVibr
ationLecture.pdf
• Remote Data Acquisition System,
http://www.aedelectronics.nl/rdas/index.htm
• Spjut, Erik, http://www.eng.hmc.edu/NewE80/
• Wang, Ruye, Inertial Navigation,
http://fourier.eng.hmc.edu/e80/inertialnavigation/
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