Damping Identification from Shock Data via Wavelet Responses

three_shocks

Structural system & component damping can measured via modal testing with applied force excitation.  One excitation method is an impulse hammer test.  Another method is a  small shaker attached to structure via a stinger rod.

Damping can also be measured by mounting the test unit on a shaker table and applying base excitation.

There is a need to estimate component damping from pyrotechnic or pyrotechnic simulation shock tests where the source energy measurements are incomplete or unavailable.  This need may arise because modal and shaker table test data is unavailable.  Furthermore, damping is nonlinear and may be higher for a pyrotechnic shock event than for a modal or shaker table test

A source shock waveform can be modeled by a series of wavelets per Ferebee R , Irvine T, Clayton J, Alldredge D,  An Alternative Method Of Specifying Shock Test Criteria,  NASA/TM-2008-215253.   This method was original develop to characterize space shuttle solid rocket booster water impact shock.  This method can be extended for natural frequency and damping measurement for shock data.

The Wavelet Response Curve-fit Methodology is appropriate for mid and far field shock measurements where modal responses appear in the accelerometer time history data.

The method is implement via the following steps:

  • Assume a series of wavelet as the base input
  • Calculate the response of one or more SDOF systems to the assumed wavelet series
  • Subtract the resulting response signal from the measured accelerometer data and calculate error
  • The goal is to repeat this process thousands of times where the to minimize the residual error
  • Each of the following parameter are varied randomly with convergence
  • For each base input wavelet: frequency, amplitude, number of half-sines, delay
  • For each SDOF oscillator response: natural frequency, damping

The method yields natural frequency and damping estimates for the response acceleration.  It also gives an estimate of the assumed base input source shock.

The method is demonstrated in the following slides.

Slides:  shock_wavelet_damping_revC.pptx

Matlab scripts & sample shock data: Vibrationdata Signal Analysis Package

avionics_shock_data.mat

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Reference Papers:

An Alternative Method Of Specifying Shock Test Criteria:
NASA/TM-2008-215253 & PowerPoint slide overview

 

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– Tom Irvine

An Indirect Method for Converting a Shock Response Spectrum Specification to a New Q Value

  •  Aerospace pyrotechnic shock response spectrum (SRS) specifications are almost always given with an amplification factor Q=10
  • Corresponding time history waveforms for the base input acceleration are almost never given with the specifications
  • Users are allowed to synthesize their own waveforms to satisfy the SRS for analysis & test purposes
  • Some shock analysis methods use the SRS directly without time history synthesis, such as modal combination methods
  • The following method enables an SRS specification to be converted to a new Q value for engineering purposes

Slides:  150_SRS_specification_new_Q.pptx

Software: Matlab Vibrationdata GUI

– Tom Irvine

Waterfall SRS, 1940 El Centro Quake

elns

wfelc

spectrogram_srs

The top figure is the time history from the El Centro earthquake, North-South horizontal component.  The middle is the corresponding Waterfall SRS with 4 second segments and with 50% overlap.  The bottom is the spectrogram.

The Waterfall SRS is calculated by first taking the complete response time history for each natural frequency of interest.  Then the time history for each is divided into segments.  Finally, the shock response spectrum (SRS) is taken for each natural frequency and for each segment, by taking the peak positive and peak negative responses.

The Waterfall SRS function is given in:

Matlab script: Vibrationdata Signal Analysis Package

>> vibrationdata > Time History > Shock Response Spectrum, Various > Waterfall SRS

See also:  El Centro Earthquake

– Tom Irvine

JPL Tunable Shock Beam

jpl_shock2

jpl_shock3

jpl_shock5

The NASA/JPL Environmental Test Laboratory (ETL) developed and built a tunable beam shock test bench based on a design from Sandia National Laboratory many years ago. ETL has been using this test system successfully since October 2008.

The excitation is provided by a projectile driven by gas pressure.

The beam is used to achieve shock response spectrum (SRS) specifications, typically consisting of a ramp and a plateau in log-log format. The intersection between these two lines is referred to as the “knee frequency.” The beam span can be varied to meet a given knee frequency. The high frequency shock response is controlled by damping material.

The tunable-beam system is calibrated with a center-of-gravity (CG) mass and footprint model of the test article. The mass simulator is mounted in the test axis with the appropriate accelerometers installed as they would be for the testing the test article. Then the system is tuned by performing test runs until the data plots meet the requirement.

Finally, the test article is mounted to the tuned beam for the actual test.

See also:  JPL Tunable Beam

– Tom Irvine

Embraer E190 Landing Shock

EMBRAER_E190_(8373095236).jpg

e190

I recently flew as a passenger on a E190 similar to the one in the top image. The landing shock is shown in the bottom image. The data was recorded on a Slam Stick X, sampled at 400 samples/sec. The initial set of peaks have a frequency of about 0.9 Hz.

Matlab File: E190_landing_shock.mat

See also: Landing Shock

– Tom Irvine

A330-200 Landing Shock

a330_200

Image Courtesy of Justin Kane

I recently flew as a passenger on a A330-200 similar to the one in the image.  I used a Slam Stick X Vibration Data Logger to measure the landing shock, with the sensor mounted on the cabin floor.  The acceleration time histories for two axes are shown in the following figures.

a330_200_landing_fore_aft

a330_200_landing_vertical

The vertical axis response has several spectra between 0.5 and 2.0 Hz.

A330-200 Landing Shock Matlab file

See also:  Landing Shock

– Tom Irvine

A320 Landing Shock

a320_jb

I recently flew as a passenger on a A320 similar to the one in the image.  I used a Slam Stick X Vibration Data Logger to measure the landing shock, with the sensor mounted on the cabin floor.  The resulting acceleration time history is shown in the following two figures, longer and shorter views.  The main wheels touch down at the zero second mark. The nose wheels contact the runway about 3.5 seconds later.

logan1

logan2

The higher frequency energy between zero and 0.5 seconds consists of components in the 10 to 15 Hz frequency domain, likely representing structural modes.  The sample rate was 400 samples per second.

A320 Landing Shock Matlab file

See also: Landing Shock

– Tom Irvine

SRS Synthesis – New Option

wdecay

(Click here for better image of Matlab GUI screenshot)

I have added an “Exponential Decay” option to the wavelet synthesis function in the Matlab GUI package.  The goal is to synthesize a wavelet series that has a gradual overall exponential decay, somewhat similar to an actual pyrotechnic or seismic shock event. Here is an example.

The advantage of using wavelets as a basis is that each has zero net velocity and zero net displacement, as does a complete series.  These conditions are needed for both analysis and testing.

Note that some pyrotechnic SRS specifications begin at a natural frequency of 100 Hz. A good practice is to extrapolate the specification down to 10 Hz, especially if there are any vibration modes below 100 Hz.

The Vibrationdata Matlab GUI package is given at: Vibrationdata Matlab Signal Analysis Package

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I previously came up with a method which synthesized a series of damped sines to satisfy an SRS.  The damped sines where then decomposed into a wavelet series.  The previous method is still available.   See Webinar 27 – SRS Synthesis

– Tom Irvine

Shock and Vibration Severity Thresholds for Structures and Equipment

Launch vehicle and spacecraft equipment must withstand pyrotechnic shock from stage separation and other flight events.   Civil engineering structures and equipment must survive seismic events.  There are many other examples where military, automotive, telecommunication and other equipment must be designed and tested to meet shock requirements derived from field or flight data.  The likelihood that a structure or equipment piece will fail a shock environment is often expressed in terms of a severity threshold.  The threshold may be expressed in terms of a base input or response level.  The purpose of this paper is to compile severity acceleration and velocity thresholds for both equipment and buildings into a single document for comparison purposes.

Link:  shock_vibration_severity_thresholds.pdf

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See also:
Shock Severity Limits for Electronic Components
Dr. Howard Gaberson’s Papers
Stess-Velocity Relationship

– Tom Irvine

Hypersphere SRS

hsrs

Figure 1. El Centro Earthquake 1940, Peak Pseudo Velocity, 36.4 in/sec
 
Launch vehicle and spacecraft equipment must withstand pyrotechnic shock from stage separation and other flight events. Civil engineering structures and equipment must survive seismic events. There are many other examples where military, automotive, telecommunication and other equipment must be designed and tested to meet shock requirements derived from field or flight data. The specification is commonly given as a shock response spectrum (SRS). An SRS may be calculated for each orthogonal input axis, assuming the availability of triaxial accelerometer data. Each axis may thus have a separate specification. Alternatively, a maximum envelope can be drawn over the three SRS curves and then applied as a uniform specification to each orthogonal axis.

The uniform enveloping method, however, can underestimate the maximum resultant shock when all possible orthogonal axes sets are considered. The purpose of this paper is to introduce a hypersphere method to achieve a true maximum SRS.

Paper link:  hypersphere_SRS

The Matlab script for this calculation is included in the GUI package at:
Vibrationdata Matlab Signal Analysis Package

– Tom Irvine