EM 67 - Recommended Practices for a Bump Test

6Vibrations Vol 28 No 3 September 2011

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frequency response curve supplied by the manufacturer isneeded to choose a suitable hammer and tip for the proposedimpact test.

Recommended Practices for a Bump TestThese practices for implementing a successful bump test resultfrom extensive research and discussions with practicingvibration specialists.

When the hammer is struck, avoid middle or end positionsof the structure. They may be nodal points of the lowerfundamental natural frequencies.

Do not strike too hard; try to stay within the linear elasticregime of the structure. Strike gently at first, then graduallyharder if necessary.

Check the impact force time waveform; a double hit willappear as a double peak.

Check the impact force spectrum; it should be flat withinthe frequency span of interest. A 20 dB drop from the initial

Although the bump test is one of the most fundamental methodsused to determine the natural frequencies of a structure, notmuch literature is available regarding the detailed proceduresand techniques required for an accurate reading of naturalfrequencies. A series of recommended practices for conducting asuccessful bump test are summarized in this article. An exampleillustrates their application for the accurate assessment of naturalfrequencies.

If an exciting frequency matches a structural naturalfrequency, resonance occurs. At resonance, vibration amplitudecan be controlled only by damping; however, artificially-introduced damping is not preferred because it consumesenergy. In general, resonance should be avoided in any system.

In addition, structural natural frequencies should be separatedfrom potential exciting frequencies. A 15% separation margin iscommonly recommended [1] although a 20% margin isadvisable in some specific applications; e.g., the special purposegear unit in API Standard 613 [2]. An accurate reading ofstructural natural frequencies of a system with a bump test is aprerequisite to any code-compliant system design or designmodification.

Instrumentation for a Bump TestThe following instrumentation is required to carry out a bumptest.

FFT (Fast Fourier Transform) vibration analyzer withcross-channel functions such as transfer function andcoherence features [3].

Instrumented hammer (a hammer with a force sensorembedded inside) with multiple tips of different size andhardness.

Vibration sensors; e.g. accelerometer.Careful selection of a suitable hammer and tip is important for

a successful bump test. In general, a softer (often also larger)hammer tip provides higher amplitudes of exciting frequencycomponents of the impact force, a narrower force spectrum, anda lower exciting frequency. Figure 1 contains a series of samplefrequency response curves for an impact hammer with tips ofdifferent size and hardness. For a specific hammer, a detailed

Recommended Practices for aBump Test

Jianke Wang, Ph.D., P.E.National Oilwell Varco

Conroe, Texas [email protected]

Summary. Procedures for conducting an impact testare reviewed. They include hammer selection,impacting location and force, and analyzer setup. Anexample provides details for interpreting test results,especially with regard to phase.

Figure 1. Frequency Response Spectra for a Hammerwith Various Tips.

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low-frequency peak is generally sufficient. If the spectrumis not flat, change to a harder hammer tip (or even to abigger hammer if necessary) to assure a flat force spectrumwithin the frequency span of interest.

Check the response (vibration) time waveform. Theresponse should taper off to zero within the time span. Ifnecessary, adjust the FFT lines and frequency span toextend the span of the time waveform.

Try a rectangular/no window first. If the response timewaveform is too noisy, use a force or exponential windowfor the original signal collected.

Auto ranging is not recommended. Always check thesignal; no over-loading (clipping of the time waveform) ofthe FFT analyzer should occur. If overloading exists,increase the range manually.

Take several averages (three is often recommended) toreduce spurious noise.

Mark and reference the sensor and hammer positions,especially when multiple positions have been tried or a tri-axial sensor has been used.

For a system under ideal conditions with one naturalfrequency, a 180 phase shift occurs across the naturalfrequency. However, single-frequency systems do not occur.Even for the simplest single spring-mass system, many naturalfrequencies of the spring itself exist. In addition, it is impossibleor not practical to eliminate all environmental noise during abump test. Therefore, in reality, not all peaks in the magnitudeplot of the force/response transfer function (inertance, mobility,or dynamic compliance) are actual natural frequencies of thesystem measured.

Several practices are recommended to confirm that the peakfrequency in the plot of the selected transfer function is anexcited system natural frequency.

A minimum phase shift of 30 to 45 in the phase plot ofthe transfer function is recommended.

A minimum coherence of 0.8 between the input (impactforce) and output response (vibration) at that frequency isrecommended [4]. If the coherence is less than 0.8, thepeak could be a consequence of either background orelectrical noise if the test has been carried out correctly.

If necessary, the phase plot of the transfer function can beflipped from the wrapped phase (within [-180, 180], thedefault setup in most FFT analyzers) to the unwrapped one.This may occur when two consecutive peak frequencycomponents are very close to each other.

According to Baxter [4] coherence in a linear system is ameasure of the causality between the input and output/responsesignals. It represents the fractional portion of the output signalpower that results from the input signal at a specific frequencycomponent. For a linear and ideal system with a single input andsingle output, the coherence between two signals will be equalto one. For two signals that are completely unrelated, thecoherence will be zero. If the coherence is less than one butgreater than zero, either noise is entering the measurements orthe system has been struck too hard and attained a nonlinearregime.

Three types of transfer functions between the input signal(force) and output response (vibration) are commonlyrecommended to identify the natural frequencies of a system.They include inertance (also called accelerance, which is theratio of acceleration response over impact force input), mobility(velocity response over impact force input), and dynamiccompliance (displacement response over impact force input).The selection of the transfer function is based on the strength ofthe measures (acceleration, velocity, or displacement) atdifferent frequencies and the value of the dominant excitingfrequency. Dynamic compliance is usually recommended forlow-frequency applications (less than 20 Hz). The transferfunction of inertance/accelerance is used for relatively high-frequency applications (greater than 1,000 Hz). For intermediateexciting frequencies, the transfer function of mobility ispreferred [3].

Example Results and DiscussionAn example illustrates the application of the techniques toaccurately assess the natural frequencies of a system.

Figure 2 shows a setup for a shale shaker bump test. Aninstrumented hammer, a tri-axial accelerometer, and an FFTanalyzer with cross-channel features are used to collect the dataof the impact force input and vibration response. Theaccelerometer and hammer have been moved to obtain the bestsignal. The operating frequency of the shale shaker is 30 Hz;therefore, mobility (the ratio of velocity response to force input)is utilized to identify the natural frequencies of the excitedsystem. Single integration of the acceleration measured is usedto obtain the velocity signal. Frequency resolution was set to0.125 Hz with a frequency span of 200 Hz, 1,600 FFT lines, anda uniform window (Editors note: Resolution is calculatedwithout the Vibration Institutes recommended factor of two.)

Figure 3 contains a set of results from the shaker setup inFigure 2. In Figure 3, x represents vibration response in thelongitudinal direction; y is vertical direction, and z is lateraldirection. The impact force is represented by f; T is the timewaveform, and S represents the spectrum. H refers to thetransfer function between two signals. C is the coherencebetween two signals.

In Figure 3 the impact force, a flat force spectrum, and theclassical (exponentially decaying) time waveforms of the impactresponses in the longitudinal, vertical, and lateral directionsverify that the impact test results are valid.

Figure 2. Shaker Bump Test Setup.

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Figure 3. Results of the Shaker Test Setup in Figure 2.

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In some cases, a wrapped phase plot within [-180, 180]might cause confusion with the phase shift around a naturalfrequency. In Figure 3, the phase plot of the transfer function inthe longitudinal direction has been flipped from the wrappedphase within [-180, 180], which is the default setup in mostFFT analyzers, to the unwrapped one.

Figure 4 shows that an unwrapped phase plot is preferred inthe longitudinal direction. The top of Figure 4 is a wrappedphase plot. Abrupt changes occur from -180 to 180 around thepeak amplitudes, especially at the peak frequencies of 40.88 Hzand 48.75 Hz. They could cause misreading of the phase shift.In this example, the unwrapped phase plot shown in the bottomof Figure 4 is preferred.

On the other hand, although many abrupt changes occur inthe wrapped phase plot in the lateral direction (see Figure 3), anunwrapped phase plot results in even poorer resolution of thephase reading due to the huge phase angle span ranging from-800 to 180.

In Figure 4, the three peak frequencies of 5.000 Hz (#7),5.375 Hz (#8), and 6.125 Hz (#9) are not considered excitednatural frequencies of the shaker basket because the phase shiftaround each peak is less than 30. The peak at 0.125 Hz isexactly on the first non-zero bin of the FFT spectrum; near-zeroHertz digital integration issues are present in most FFT

analyzers. In addition, the lower frequency limit of theaccelerometer response is off by 3 dB at 0.5 Hz; the 0.125 Hztherefore cannot be confirmed as a natural frequency of theshaker basket.

According to the recommended practices described in thisarticle, the first eight fundamental natural frequencies of theshaker basket shown in Figure 2 are measured as 0.5 Hz,1.25~1.50 Hz, 2.0~2.125 Hz, 2.875 Hz, 3.5~3.625 Hz,4.125~4.250 Hz, 40.88 Hz, and 48.75 Hz.

The finite element method (FEM) in ANSYS was used in apre-stressed modal analysis of a simplified shaker basket model(no fillet welds are included) to show that the first eightfundamental natural frequencies are 0.30 Hz, 0.46 Hz, 1.31 Hz,2.93 Hz, 4.05 Hz, 4.34 Hz,, 38.74 Hz, and 43.80 Hz [5]. Thetest results match the predicted ones. If all fillet welds areincluded in the shaker basket model, the slight differencesbetween the predicted and measured natural frequencies will beeven smaller [5]. The reason is that the fillet welds increase thelocal stiffness of each weld [6]. In other words, with all filletwelds included in the FEA model, the natural frequencies of therigid modes will decrease and those of the flexible modes willincrease [5].

ConclusionThis article presents a series of recommended practices that arecrucial to an accurate reading of the natural frequencies of anystructure or system. An example illustrates the application ofthese recommendations so that the excited natural frequencies ofthe system can be differentiated from environmental or electricalnoise.

AcknowledgmentThe author wishes to thank NOV Brandt R&D Department fortheir help during the bump and related testing.

References1. Eshleman, R.L., Vibration Control, Advanced VibrationAnalysis, Vibration Institute (2006).

2. American Petroleum Institute, Special Purpose Gear Units forPetroleum, Chemical, and Gas Industry Services, API Standard613 (2003).

3. Eshleman, R.L., Basic Dual Channel Testing, MachineryVibration Analysis: Diagnostics, Condition Evaluation, andCorrection, Vibration Institute (2002).

4. Baxter, N.L., Field Application of Dual Channel andSynchronous Time Averaging Analysis Techniques, AdvancedVibration Analysis, Vibration Institute (2006).

5. Wang, J.K., Virtual Prototyping plus Physically-TestedValidation Delivers State-of-the-Art Shale Shakers, Proceedingsof NAFEMS World Congress 2011, Boston, USA (2011).

6. Det Norske Veritas, Fatigue Design of Offshore SteelStructures, DNV Recommended Practice DNV-RP-C203(2010).

Figure 4. Reduction of Outboard Spindle Bearing SpikeEnergy after Lubrication.

Wrapped Phase Plot

Unwrapped Phase Plot

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EM 67 - Recommended Practices for a Bump Test