THE NASA ENGINEERING & SAFETY CENTER (NESC ... Vibration: Gemini Program Titan II Pogo Astronaut Michael Collins wrote: The first stage of the Titan II vibrated longitudinally, so

© The Aerospace Corporation 2010© The Aerospace Corporation 2011

Dynamic Concepts, Inc.

Huntsville, Alabama

THE NASA ENGINEERING

& SAFETY CENTER (NESC)

SHOCK & VIBRATION TRAINING PROGRAM

By

Tom Irvine, Dynamic Concepts, Inc.

And

Dr. Curtis E. Larsen

NASA Technical Fellow for Loads and Dynamics


NESC is an independently funded program with a dedicated team of technical experts

NESC was Formed in 2003 in response to the Space Shuttle Columbia Accident Investigation

NESC’s fundamental purpose is provide to objective engineering and safety assessments of critical, high-risk NASA projects to ensure safety and mission success

The National Aeronautics and Space Act of 1958

NESC is currently expanding its services to benefit United States:

MilitaryGovernment AgenciesCommercial Space


NESC Engineers Provide a Second Pair of Eyes

Design and Analysis Reviews

Test Support

Flight Accelerometer Data Analysis

Tutorial Papers

Perform Research as Needed

NESC Academy

We already have a charge number.


NESC Sample Projects

NASA/Wallops

Terrier-Black

Brant Flight

Orion LAS PA-1 Test

NASA/Stennis

A-3 Test Stand

5e-mail address

Department/subdivision name

Dynamic Concepts, Inc.

Huntsville, Alabama

The authors have prepared self-study course units for:

• Shock

• Vibration

• Acoustics

• Structural Dynamics

• Signal Processing

These taxpayer-funded materials are available upon request to U.S. civil servants and contractors working on NASA, commercial space, and military projects.

6e-mail address


Students learn best by doing!

Challenges

Most engineering students do not take a vibrations course in college

College-level vibration courses focus on theory rather than on practical applications

Pedagogy . . .

These NESC course units contain

Slide presentations

Software exercises using actual accelerometer data samples & synthesized time histories

Software is mainly written in Matlab with some visual C++ programs

Students keep software for use on their own projects, including source code

7e-mail address


Work-in-Progress . . . 18 Units completed, hundreds more to go!

Topics (planned or completed)

Signal Identification, Natural Frequencies, and Damping Ratios

Structural Dynamics, Rods, Beams & Plates

Avionics Isolation Octave Rule Sine & Sine Sweep Vibration Random Vibration Fourier Transforms Power Spectral Density Shock Response Spectra Vibration Response Spectra Fatigue, Miners Rule, Rainflow Steinberg Electronic Formulas Aliasing, Nyquist Frequency Digital Filtering Sound Pressure Levels Finite element methods

8e-mail address


Wind speed of 42 miles per hour

Torsional vibration mode at 0.2 Hz.

The two halves vibration 180° out-of-

phase.

Torsion mode response due to

aerodynamic self-excitation.

Not due to resonance.

Strouhal frequency

fs = S U/D

fs = 0.84 Hz at 42 mph

0.2 Hz oscillation sinusoidal with an amplitude up to 28 feet.

Acceleration = ω^2 Displacement

0.5 (336 in peak-to-peak ) [ 2 0.2 Hz ]^2 (1 G /386 in/sec^2 )

= 0.69 G

Tacoma Narrows Bridge 1940

9e-mail address


Sine Vibration: Gemini Program Titan II Pogo

Astronaut Michael Collins wrote:

The first stage of the Titan II vibrated longitudinally, sothat someone riding on it would be bounced up anddown as if on a pogo stick. The vibration was at arelatively high frequency, about 11 cycles per second,with an amplitude of plus or minus 5 Gs in the worstcase.

10e-mail address


Suborbital Launch Vehicle Flight Accelerometer Data

-50

-40

-30

-20

-10

0

10

20

30

40

50

0 5 10 15 20 25 30 35 40 45 50 55 60 65

TIME (SEC)

AC

CE

L (

G)

FLIGHT ACCELEROMETER DATA

Liftoff Transonic, max-Q ACS Thrusters

11e-mail address


Pegasus Drop Transient – Damped Sinusoid

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

-1 0 1 2 3 4 5 6

Input DataSynthesis

TIME (SEC)

Accel(G)

Results

Case Amplitude fn(Hz) damp Phase(rad) Delay(sec)

1 0.7306 9.5715 0.0118 3.8999 0.1055

How does the octave rule apply?

12e-mail address


FFT Sound Pressure from an Apache Helicopter Fly-over

Main rotor hub frequency = 5.25 Hz & BPF = 21 Hz (Doppler shifted)

13e-mail address


Sounding Rocket Flight Accelerometer Data

Waterfall FFT Ch 1 X-axis 36.258 Mission

Frequency (Hz)

Time (sec)

Waterfall FFT 3D Plot - Time, Frequency, Magnitude

Fundamental body-bending frequency 10 to 13 Hz.

Rigid-body rotation frequency at 4 Hz.

Terrier-Black Brant

14e-mail address


Power Spectral Density

NAVMAT P9492 level

Learn how to calculate the overall GRMS level

G^2/Hz is really GRMS^2/Hz

15e-mail address


Division/OrganizationJune 7–9, 2011 – 18 point Arial

Synthesize time history to satisfy NAVMAT P9492 level

Also take histogram to verify normal distribution (histogram plot omitted for brevity)

Power Spectral Density Overall Level = 6.06 GRMS

Accel(G)

Time (sec)

Accel(G^2/Hz)

Frequency (Hz)

Useful for

Understanding how a vibration control computer generates a signal for a PSD

Performing modal transient and rainflow cycle fatigue analysis

Synthesized Base Input

16e-mail address



SDOF System Response to Base Input

m

k c

x

y

Useful for

Apply synthesized time history as base input to SDOF system

Calculate modal transient response using a Digital Recursive Filtering Relationship

Same numerical engine as used in the SRS calculation

mass

damping coefficient

stiffness

acceleration of mass

base acceleration

17e-mail address



SDOF Acceleration Response, fn=200 Hz, Q=10, 11 GRMS SDOF System Response to

NAVMAT Time History

Response is narrowband random.

Take histogram to verify normal distribution (histogram plot omitted for brevity)

Take PSD of input and response.

Show that overall response GRMS can also be calculated via Miles equation.

Accel(G)

Time (sec)

Accel(G^2/Hz)

Power Spectral Density

Frequency (Hz)

18e-mail address



Half-power Bandwidth

Q = fn / Δf

fn = natural frequency

Δf = frequency bandwidth for -3 dB points

Q = 200 Hz / 20 Hz

= 10

Power Transmissibility

Frequency20 Hz

Trans

(G^2/G^2)

3 dB

19e-mail address


Shock Response Spectrum

Subject a system of independent SDOF systems to a common base input

fn1 < fn2 < fn3 < … < fn L

20e-mail address



-20

-15

-10

-5

0

5

10

15

20

0 0.05 0.10 0.15 0.20

fn = 10 Hz, Q=10fn = 70 Hz, Q=10Base Input

TIME (SEC)

AC

CE

L (

G)

ACCELERATION TIME HISTORIES

TIME (SEC)

0.1

1

10

100

10 100 1000 2000

NegativePositive

NATURAL FREQUENCY (Hz)

PE

AK

AC

CE

L (

G)

SRS Q=10 10 G, 10 msec HALF-SINE BASE INPUT

Shock Response Spectrum

Calculate family of response curves with natural frequency as an independent variable.

Pick off maximum and minimum peaks for each response curve.

Make table. Plot SRS.

21e-mail address



-20

-15

-10

-5

0

5

10

15

20

0 0.05 0.10 0.15 0.20 0.25

TIME (SEC)A

CC

EL

(G

)

ACCELERATION - WAVELET SERIES

Shaker Shock using Wavelets

Optimized to Minimize Displacement, Velocity & Acceleration

1

10

100

1000

10 100 1000 2000

Spec & TolNegativePostive


PE

AK

AC

CE

L (

G)

SHOCK RESPONSE SPECTRUM Q=10

22e-mail address


Frangible Joint, 26.25 grain/ft

SRS Q=10 For Reference Only

fn (Hz) Peak (G)

Note that the specification is log-log format.

Modal transient analysis to determine response of component.

Need to synthesize a time history to satisfy the SRS.

But the time history will not be unique.

Damped Sine Synthesis to Satisfy an SRS

fn (Hz) Peak (G)

100 100

4200 16,000

10,000 16,000

23e-mail address


-10000

-5000

0

5000

10000

0 0.01 0.02 0.03

TIME (SEC)

AC

CE

L (

G)

ACCELERATION TIME HISTORY DAMPED SINUSOIDS

102

103

104

105

100 1000 10000

SpecificationNegativePositive


PE

AK

AC

CE

L (

G)

SRS Q=10 DAMPED SINUSOIDSSRS Q=10 DAMPED SINUSOIDS

ACCELERATION TIME HISTORY DAMPED SINUSOIDS

Pyrotechnic Shock Simulation for Modal Transient Analysis

TIME (SEC)


ACCEL (G)

PEAK ACCEL

(G)

24e-mail address


-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

0 0.0001 0.0002 0.0003 0.0004

Decimated, SR=78.125 KHzOriginal, SR = 2.5 MHz

TIME (SEC)

AC

CE

L (

G)

SYNTHESIZED TIME HISTORY, EXAMPLE 2

Aliasing Errors in Signal Analysis - Numerical Experiment

Aliasing occurs in the Decimated time history.

Synthesized Time History – Near Field Shock Simulation

25e-mail address


101

102

103

104

105

102

103

104

105

106

Decimated, SR=78.125 KHzOriginal, SR=2.5 MHz


PE

AK

AC

CE

L (

G)

SRS Q=10 EXAMPLE 2

Aliasing Errors in

Signal Analysis

The Decimated SRS is approximately 10 to 20 dB higher than the Original SRS. The source of the error is aliasing.


Conclusions

NESC engineers are available to help with design reviews, test support, research projects, flight accelerometer data reduction, etc.

NESC is independently funded

NESC offers shock & vibration training units, which include software programs

How may we serve you?Contact:

Dr. Curtis Larsen Email: [email protected]

Tom Irvine Email: [email protected]

Documents

THE NASA ENGINEERING & SAFETY CENTER (NESC ... Vibration: Gemini Program Titan II Pogo Astronaut Michael Collins wrote: The first stage of the Titan II vibrated longitudinally, so