Multi-axis Shock & Vibration Testing

Equipment must be designed and tested to withstand shock and vibration.  Ideally, all equipment would be tested on a shaker table with six-degree-of-freedom control (three translations and three rotations).  Such tables and control systems exist but are very expensive.  Furthermore, any multi-axis testing requires careful consideration of phase angles between the six degrees.

Another option is to test equipment on a triaxial table where the three translations are controlled, and the three rotational degrees are constrained to zero motion.  Testing on a biaxial table is yet another choice.

The most common test method, however, remains testing in each of three orthogonal axes, one axis at a time, on a single-axis shaker.  This is simplest and least expensive method.

The question arises “Should the acceleration level be increased for the case of single-axis testing?”

There is a tacit understanding that aerospace and military equipment test levels already have a sufficient uncertainty margin or safety factor so that the levels can be used without further increase.  In other words, the specifications are already intended for single-axis testing.  In many cases, a uniform level is used in each axis which is the maximum envelope of the maximum expected levels in the three axes plus some margin.

* * *

The standards which address testing equipment for earthquakes take a different approach. The following descriptions are taken from five common standards.

Only KTA 2201.4 gives a scaling formula.  This is also the only standard from the five samples which may be freely downloaded.

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IEEE 344-2013  Standard for Seismic Qualification of Equipment for Nuclear Power Generating Stations

8.6.6 Multiaxis tests

Seismic ground motion occurs simultaneously in all directions in a random fashion. However, for test purposes, single-axis, biaxial, and triaxial tests are allowed. If single-axis or biaxial tests are used to simulate the 3D environment, they should be applied in a conservative manner to account for the absence of input motion in the other orthogonal direction(s). One factor to be considered is the 3D characteristics of the input motion. Other factors are the dynamic characteristics of the equipment, flexible or rigid, and the
degree of spatial cross-coupling response. Single and biaxial tests should be applied to produce adequate levels of excitation to equipment where cross coupling is significant and yet minimize the level of overtesting where the cross coupling is not significant.

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KTA 2201.4   Design of Nuclear Power Plants against Seismic Events, Part 4: Components

This document may be freely downloaded: link

See paragraphs

5.3.3 Excitation Axes

5.5.2.5 Simultaneity of excitation directions

Simultaneous three-axis testing is preferred. But single-axis testing can be substituted by testing in each of three axes sequentially.

The standard shows, for example, that the uniform single-axis level should be the “square root of the sum of the squares” of the three orthogonal installation site levels.

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IEC 980 Recommended practices for seismic qualification of electrical equipment of the safety system for nuclear generating stations

6.2.9 Qualification test method

6.2.9.1 General

As is well known, seismic excitation occurs simultaneously in all directions in a random way. According to this point of view, the test input motion should consist of three mutually independent waveforms applied simultaneously along the three orthogonal axes of the equipment.

However, taking into account that three axial testing installations are rare and that triaxial testing is desirable when significant coupling exists simultaneously between the two preferred horizontal axis of the specimens, biaxial testing with multifrequency independent input motion in the horizontal and vertical direction is an acceptable test.

Tests shall be performed according to 6.3.2 and, in terms of total duration and fatigue induced, are intended to become conservative.

In some cases, single axis tests with multiple, or single frequency excitation are also acceptable methods of test if properly justified considering the effect of coupling between axes.

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Telcordia GR-63-CORE

Assumes single-axis testing.  The base input time history is specified in the standard.

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IEEE 693-2005 – IEEE Recommended Practice for Seismic Design of Substations

paragraph 4.9

The shaker table shall be biaxial with triaxial preferred.

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See also:

Seismic Test & Analysis Webinars

Hypersphere SRS

 

– Tom Irvine

Webinar Index

Here is a listing of the webinars and related materials.

Matlab script: Vibrationdata Signal Analysis Package

1. Natural Frequencies

2. Sine Vibration

3. Sine Sweep Vibration

4. Random Vibration

5. Fourier transforms

6. Leakage Error, Hanning Window

7. FFTs

8. Waterfall FFT

9. White Noise FFT

10. Sample Rate & Aliasing

11. Power Spectral Density

12. Power Spectral Density Functions of Measured Data

13. SDOF Response to Power Spectral Density Base Input

14. Synthesizing a Time History to Satisfy a PSD Specification

15. SDOF Response to Base Input in the Frequency Domain

16. Vibration Response Spectrum

17. SDOF Response to Applied Force

18. Force Vibration Response Spectrum

19. Digital Filtering

20. Digital Filtering, Part 2

21. Integration & Differentiation of Time Histories

22. Integration and Differentiation of Time Histories & Spectral Functions

23. Classical Shock Pulse

24. Seismic Shock

25. Pyrotechnic Shock

26. Pyrotechnic Shock, part 2

27. SRS Synthesis

28. Multi-degree-of-freedom SRS

29. Stress-Velocity Relationship

30. Rectangular Plate Shock & Vibration

31. Rectangular & Circular Plate Shock & Vibration

32. Electronic Circuit Board Fatigue

33. Rainflow Fatigue

34. Rainflow Fatigue for Continuous Beams

35. Using Fatigue to Compare Sine and Random Environments

36. Non-Gaussian Random Fatigue and Peak Response

37. Acoustic Fatigue

38. Electronic Circuit Board Fatigue Part 2

39. Sine-on-Random Vibration

40. Shock Fatigue

41. PSD Special Topics

42. Shock Special Topics

43. Two-degree-of-freedom System, Two-stage Isolation

44. Sine Filtering

45. Two-degree-of-freedom System with Rotation and Translation

46. Two-degree-of-freedom System with Multi-point Enforced Motion

47. Shock Response Spectrum Synthesis, Special Topics

Seismic Test & Analysis Webinars

Structural Dynamics Webinars

Fatigue Webinars

Circuit Board Shock & Vibration Analysis

HALT/HASS for Product Reliability

More later. . .

– Tom Irvine

Nonlinear Modeling of Bolted Interfaces & Joints

Mechanical joints may have nonlinear damping and stiffness, due to.frictional slipping between the connected members, etc.  I am enclosing modeling advice from a colleague and related links.

– Tom Irvine

* * *

If the nonlinearity stays fairly weak then there are a few options to do a worst case analysis:

1.) For broadband loads the linear model with low-level damping is usually a very conservative model for the system at high amplitude (in our cases we frequently see damping increase by a factor of 3-4). Of course if you have a sharp harmonic then you need to consider the downward shift in frequency, but that is usually small and you’re not likely to design something to have a strong excitation frequency just barely below resonance.

2.) To improve fidelity, these uncoupled 1DOF oscillator models with power-law dissipation (i.e. log(damping) vs log(displacement amplitude) = linear) can do a very good job of capturing how the damping changes with amplitude. It APPEARS (no guarantees with nonlinearity) that one can obtain a “worst case” analysis by using a linear model with damping near the maximum damping expected at that amplitude. However, a word of caution: the frequency shift smears the resonance peak, so one cannot necessarily assume that the damping measured by a half-power method will be accurate! We use a Hilbert transform or some other time domain technique to estimate damping at a time instant (and therefore at a certain amplitude). We have also used step-sine tests (in a paper for this year’s IMAC) with a phase condition to find the resonance frequency and damping with good success. In any event, an approach such as this will be less over-conservative than a linear model based on low-amplitude response and if one is careful it is probably possible to still make sure it is conservative.

3.) If there is nonlinearity then one should also think whether any nonlinear phenomena might come into play: super-harmonic resonance (exciting a mode at omega by applying a force at (1/2)*omega, (1/3)*omega, etc…; modal coupling (modes are excited that shouldn’t be based on linear theory), chaos, etc…

Dr. Matt Allen, University of Wisconsin-Madison

Dynamics of Bolted Interfaces

Numerical Study Iwan Model

Nonlinear Characterization of a Bolted Structure

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See also:

Some Nonlinear Sine Sweep Vibration Test Data 

Tall Building Natural Frequencies and Damping

Seismic Test & Analysis Webinars

This is a work-in-progress…

I am creating a series of webinars with Matlab exercises for seismic testing.

Here are the slides.

Telcordia Technologies Generic Requirements GR-63-CORE:  Bellcore_GR_63_Core.ppt
This unit contains an alternative waveform for VERTEQII.

CEI.IEC 980, Recommended practices for seismic qualification of electrical equipment of the safety system for nuclear generating stations:  CEI/IEC 980: 1989

IEEE Std 693-2005, Recommended Practice for Seismic Design of Substations: IEEE_693_sine_beat.pptx

IEEE Standard for Seismic Qualification of Equipment for Nuclear Power Generating
Stations: IEEE_std_344.ppt

Matlab script: Vibrationdata Signal Analysis Package

* * *

See also:

Cummins Generator Seismic Shaker Test

Earthquake Conference

Seismic Shock

Webinar 47 – Shock Response Spectrum Synthesis, Special Topics

Seismic Peak Ground Acceleration

Some Earthquake Engineering Terminology

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– Tom Irvine

Shock & Vibration Courses, Trieste, Italy & Singapore

You are welcome to participate in any of the following courses.

I will teach shock & vibration course in Trieste, Italy on January 25-27, 2017.   Course Link

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I will teach a shock & vibration finite element analysis course in Singapore, February 13-15, 2017.  Brochure Link

Thank you,
Tom Irvine

Structural Dynamics Webinars

This is a work-in-progress…

I am creating a series of webinars with Matlab exercises for structural dynamics and finite element analysis.

Here are the slides:

Unit 1  Basic FEA

Unit 2  Damping

Unit 3 Modal Analysis

Unit 4 Transfer Functions

Unit 5  Transient Analysis

Unit 6  Applied Force Response Analysis

Unit 7  Response to Seismic Base Mass Excitation

Unit 8  Response to Enforced Motion

Unit 9  Beam Bending FEA

Unit 10 Beam Bending FEA with Added Mass and Stiffness

Unit 11 Beam Bending FEA with Steady-State Sinusoidal Base Excitation

Unit 12 Beam Bending FEA with Sine Sweep Base Excitation

Unit 13  Beam Bending FEA with PSD Base Excitation

Unit 14  Beam Bending FEA Fatigue

Unit 15  Beam Bending FEA Shock

Unit 17  FEA: Circuit Board Natural Frequencies

Unit 18  FEA: Circuit Board Damping

Unit 19  FEA: Circuit Board Response to Sine Vibration

Unit 20  FEA:  Circuit Board Response to Sine Sweep Vibration

Unit 21  FEA:  Circuit Board Response to Random Vibration

Unit 22  FEA:  Circuit Board Response to PSD Synthesis

Unit 23_FEA:  Circuit Board Shock Response Spectra & Synthesis 

Unit 24_FEA:  Circuit Board MDOF Shock

Unit 25:  FEA:  Circuit Board Fatigue

Special Topic:  Irvine_multiaxis_fatigue.pptx

Matlab script: Vibrationdata Signal Analysis Package

* * *

See also:

Transfer Functions from Normal Modes

Convert Modal Damping to a Damping Coefficient Matrix

Beam Bending, Finite Element Analysis

The Mode Acceleration Method  MA_method.pdf

The Modal Truncation Augmentation Method:  MTAM.pdf
This is also known as the residual vector method.  

* * *

– Tom Irvine

Satellite Equipment Vibration Testing

stentor__1

Stentor Satellite

Equipment mounted in satellites must withstand acoustic-driven random vibration at liftoff and during the transonic and maximum dynamic pressure phases of flight.   The equipment must be designed and test accordingly.

The equipment is mounted on shaker tables for the random vibration testing, but this can be overly conservative with respect to the actual vibroacoustic environment.

Here is an interesting case study paper:

Comparison of Satellite Equipment Responses Induced by Acoustic and Random Vibration Tests, Bertrand Brevart, Alice Pradines, 2002. Comparison_Satellite_2002.pdf

Force-limiting is one method for mitigating this overtest problem.  See NASA-HDBK-7004

More later…

– Tom Irvine

A320 Takeoff Vibration

8096965_ff12ee2c26_b

Figure 1.  A320 Takeoff

I recently flew as a passenger in an A320 similar to the aircraft shown in Figure 1.

a320_takeoff_alt

 

Figure 2.  Time History Plots

The takeoff vibration is shown in Figure 2 for the lateral and vertical axes.   The aircraft went airborne at 393 seconds.  The fore-aft axis is omitted since its level was lower.  The sensor was a Slam Stick X mounted on the cabin floor.

a320_takeoff_2

Figure 3.  PSD, Lateral Axis

a320_takeoff_3

Figure 4.  PSD, Vertical Axis

The PSD plots show some distinct spectral peaks which are most likely forcing frequencies, or possibly lightly-damped structural resonances.

Here is the time history data file:  takeoff_data

– Tom Irvine

Some Nonlinear Sine Sweep Vibration Test Data

Certain equipment must be designed and tested to withstand external vibration excitation.  This is common in the military, naval, aerospace and other industries.

The equipment is typically mounted on a shaker table and subjected to base excitation.  The input may be random vibration if the field environment is likewise.  In other cases, random vibration is used to verify the integrity of parts and workmanship separately from the maximum expected field environment.

The random vibration is typically specified as a power spectral density (PSD).  Note that the workmanship screen and field level can be enveloped by a single PSD. A goal is to verify that the equipment operates properly before, during and after the random vibration test.

A more thorough test is to perform a sine sweep test before and after the random vibration test.   A response accelerometer is mounted on the test article, in addition to the control accelerometer at the base input location.   The objective is to determine whether any natural frequencies have shifted, or any other changes have occurred, as a result of the random test.  Such changes could indicated loosened fasteners, crack formation or other defects.

A case history is given next.  The data was sent to me by a colleague.  I have requested further information on the equipment and will post a photo or diagram later if permission is granted.

sine_sweep_nonlinearity

Figure 1.

sine_sweep_fft
Figure 2.

A rocket engine assembly was subjected to a sine sweep test in conjunction with a random test.  A resonant response occurred when the excitation frequency was swept through 85 to 86 Hz as shown in Figure 1.  The equipment response would have had a similar frequency content to the input if it had been a well-behaved, linear, single-degree-of-freedom system.  The response Fourier transform for the corresponding duration did have a spectral peak at 85.45 Hz matching the sweeping input frequency as shown in Figure 2.

(Note that this is an approximation because the Fourier transform is taken over a short duration and represents an average, whereas the input frequency has instantaneous change.)

But the response also showed integer harmonics with the highest peak at 683.6 Hz, which was 8x the fundamental frequency.

Please let me know if you have observed similar effects or have other insights.  Hopefully, I can post more details later…

Sine Sweep Time History Data

Thank you,
Tom Irvine

* * *

My colleague Albert Turk sent me a reply, paraphrased as follows:

I suspect a component with a resonance at the input frequency that is excited to the point of metal-to-metal impact. I have seen data from repetitive impact machines (HASS) and also from gunfire (50 cps) that had these integer multiples.

If so, the sinusoidal excitation has turned the assembly into a repetitive impact machine near 85 Hz. It would be interesting to see if there is a sine input amplitude threshold below which this suddenly goes away.

And Steve Zeise wrote:

I have observed this phenomenon and tracked it down to loose joints introducing impacts into the system.

Note that joints can slip under shock & vibration loads.

“Loss of clearance” of “loss of sway space” may be appropriate, related terms to describe the problem shown in the data.  Further investigation is needed.