[Mechanisms and Machine Science] Vibration Engineering and Technology of Machinery Volume 23 || Qualification of Large Structures for Shock Loads

Qualification of Large Structuresfor Shock Loads

K.K. Meher and A. Rama Rao

Abstract Many critical equipments and components have to withstand shock andvibration during its life time. In defence, space and nuclear industries in particular,it is mandatory to test and analyze such components before acceptance. Analyticaland experimental qualification of these components is an important exercise to befulfilled as per the applicable codes and practices. Test for shock qualification isparticularly important for components designed for defence and space applications.When the structure is large, generally an analytical approach is followed and a smallscale model is experimentally validated for such qualification and the result isextended to the prototype. This approach may or may not be true always. The paperdiscusses about the phases of qualifying a large component for a certain level ofshock. Achieving the required shock level and the pulse duration experimentallywith repeatability is a challenging task. Besides, when the size and shape of thestructure is odd, the qualification procedure becomes more complicated and at timesdifficult to achieve the desired objective. The objective was to achieve the requiredshock pulse by dropping the test structure from a predetermined height on a targetmade of commercially available rubber material. The test object is a long stainlesssteel vessel weighing 805 kg and 2.8 m long. The vessel is housed in a rigid cagewith arrangement to lift with a magnetic clutch for instantaneous release fordropping. It was required to subject the vessel to both vertical and horizontal shockof 25 g of 35 ms duration. For dropping the vessel horizontally, the housing cagewas dropped on more than one target from a predetermined height. The procedurefollowed in arriving at the drop height, actual drop height and the achieved shocklevels are discussed in the paper.

Keywords Shock test � Shock pulse � Shock signal � Shock qualification � SRS

K.K. Meher (&) � A. Rama RaoVibration Laboratory Section, Reactor Engineering Division, Bhabha Atomic ResearchCentre, Mumbai 400 085, Indiae-mail: [email protected]

A. Rama Raoe-mail: [email protected]

© Springer International Publishing Switzerland 2015J.K. Sinha (ed.), Vibration Engineering and Technology of Machinery,Mechanisms and Machine Science 23, DOI 10.1007/978-3-319-09918-7_17

195

1 Introduction

Many critical components and equipments designed for space, defence and nuclearapplications have to undergo mandatory qualifications [1, 2] test for shock andvibration prior to their actual acceptance. Qualification for shock is one of the mostimportant tests done both by analytical and/or experimental tools [2–4]. When thestructure is large, generally an analytical approach is followed and a small scalemodel is experimentally validated and the result is extended to the prototype. Thisapproach may or may not be true in all the cases. There are many guidelines andstandards [1–5] available for performing such tests for design qualifications.Though there are many standard procedure and facilities available to cater for smallsize component testing [5], one has to tailor the procedure to fit the designrequirement especially when the components are very big and cannot be tested bythe available conventional facilities. There are many references in this area [6–9]which address specific problems related to structural dynamics. A Bertram [9]suggests a method for dynamic qualification of large structure.

The test discussed in this paper is experimental shock testing [10, 11] of a vesselweighing 805 kg and 2.8 m long for a 25 g shock level and 35 ms pulse duration asshown in Fig. 1. Achieving the required shock level and the pulse durationexperimentally with repeatability was a challenging task.

Over and above, the shape and size of the structure to be tested made theprocedure more complicated and at times difficult to achieve the required shockthroughout [10, 11]. The vessel housed in a rigid cage is lifted to a predeterminedheight [12] and dropped on a specially designed target.

The vessel was tested in all three directions (one vertical and two horizontal) forthe required level of shock [10]. The signals acquired from different parts of the testvessel show different levels for the same drop height due to secondary interactionand complex response of different parts. The complexity of the tests was not only

Fig. 1 The required idealshock pulse

196 K.K. Meher and A. Rama Rao

with the levels and repeatability, but also with the high frequency content of thesignal emanated by metallic interaction during and at the time of touching thetarget. The signal processing [3] needs special filtering techniques to get usefulsignal from the acquired data. Also, the tests appears more inconsistent in certaindirections as regard to the level, duration and repeatability and need an engineeringdecision to validate the qualification for the required goal.

This paper addresses the issues of consistency in shock level and duration,repeatability and noisy signal during such a shock test as experienced in the case[10].

2 The Test Vessel and Dropping Arrangement

The test vessel [10] is a cylindrical housing for testing individual components. Thecomponents are introduced in the vessel and assembled such that it simulates theconditions surrounding the component in actual use. Figure 2 shows the schematicof the test vessel with its supporting cage structure for tests in vertical direction andFigs. 3 and 4 for horizontal direction. The test vessel along with the supporting cageweighs 805 kg and 2.8 m long. The test vessel has two flanges one on top and one

Magnetic Clutch

Sensor 3

Sensor 2

Sensor 1

Deck of rubber pads

Test

Supporting Frame

Fig. 2 Schematic of the testvessel with supportingstructure for test in verticaldirection

Qualification of Large Structures for Shock Loads 197

in the middle. Provision for rigid mounting of shock measuring accelerometers forsensing vertical and horizontal shock was made on the two flanges of the vessel andat the bottom. Mounting positions are accordingly chosen. The vessel is lockedinside the cage allowing minimum relative motion between the cage and the vessel.A magnetic clutch lifts the cage and releases it as and when required. In verticaldirection the cage gets guided to fall vertically, however for horizontal test therewas no guiding arrangement.

3 Analytical Estimation of Drop Height

Theoretical calculations assuming rigid floor, rigid cage, and ideal fall shows a dropheight of around 0.35 m required to achieve the shock of 25 g and 35 ms duration.An analytical estimation of the drop height has been given below based on theoryand practical experiences.

The cage has been idealized as a free falling mass from a height (h) on agrounded spring (simulated ground condition with stiffness k) for analyzing its

Magnetic Chuck

Test Vessel

Balancing

Rubber Decks

Sensor 1 Sensor 2Sensor3

Support platforms

Supporting Cage

Fig. 3 Schematic of the test vessel with supporting structure for horizontal tests

Support platformsRubber Decks

Balancing Flange

Supporting Structure

Test Vessel Sensor3Sensor 2Sensor 1

Magnetic Chuck

Fig. 4 Schematic of the test vessel with supporting structure with balance flange


dynamic behavior. The idealized system is shown in Fig. 5. The response [13] fromsuch a system with approach velocity of

ffiffiffiffiffiffiffiffi

2ghp

is given by

x tð Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2ghx2 þ g

x2

� �2r

sinðxt� /Þ þ gx2 ð1Þ

and

x::tð Þ ¼ �x2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2ghx2 þ g

x2

� �2r

sinðxt� /Þ ð2Þ

where,x tð Þ Displacement response with time (t)€x tð Þ Acceleration response with time (t)g Acceleration due to gravityω Natural frequency of the idealized spring mass system/ Phase angle

Recognizing the fact that, gx2 ¼ dst (the statical deflection) and the maximum

acceleration occurs when the sine function is 1, which leads to a direct relationship[13] between the drop height and the acceleration as

€xg¼ �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2hdst

þ 1

r

ð3Þ

For the shock pulse duration of 35 ms (half sine pulse), the time period is 70 ms.This leads to natural frequency (ω) of 89.76 rad/s. With a total drop weight of805 kg (vessel along with the supporting cage), the calculated stiffness (k) is6485.77 KN/m. From relationship 3, the drop height (h) for 25 g shock level is0.35 m.

Mass (m)

Mass

Spring Stiffness

ν = √2gh

(k)

Height

Fig. 5 Drop heightestimation for an idealizedspring-mass system


However, due to variations in as installed conditions, the drop height is expectedto vary [12]. In the above idealized calculation, damping has not been consideredwhich will appear in the form of stain energy, heat, sound and structural damping ofthe falling mass. These considerations will ask for a higher drop height than theideal calculation [12]. The calculated stiffness from the above relationship is thedynamic stiffness which is 1.4 times higher than the static stiffness [12].

Kshock ¼ 1:4Kstatic ð4Þ

From relationship 4, the static stiffness Kstatic comes out to be 4632.7 KN/m.Using the static stiffness for calculating static deflection dst, leads to the new dropheight of 0.49 m. The actual and theoretical drop heights also have a similarrelationship as shown below.

Hactual ¼ 1:4Hideal ð5Þ

The target is a stack of commercial grade rubber pads that together givesdynamic stiffness close to calculated dynamic stiffness. The calibration trials werecarried out to account for all the ground variables to arrive at a conservative dropheight to achieve the required shock pulse.

4 The Shock Test Procedure

As shown in Figs. 2, 3, and 4, all the three accelerometers measure the shock in thedirection of test and so responses from all the three sensors are analyzed to assessuniformity of the shock loading. Variations in the amplitude of shock amplitude atthe three locations were expected due to unsymmetrical participation of masses.

The recorded signals were analyzed online, with a standard FFT analyzer andMATLAB. The undulations in the signals are due to the high frequency compo-nents arising during impact. With proper filtering of the signal, the actual half sinesignal is obtained. Tables 1 and 2 show the trial data of the tests and Figs. 6, 7, 8,and 9 show both unfiltered and filtered signals from the tests.

5 Observation from the Vertical Test

For the vertical tests, the assembly was made to fall on a deck of rubber pads (eachlayer having a thickness of 12 mm). The acceleration levels and the pulse durationsfor different height are tabulated in Table 1. The final height of drop required forachieving the required amplitude of shock on 13 layers of rubber pads was 0.5 m.This is close to the calculated height in Para 3. This height and the rubber pad


combination give an acceleration level of 25 g and time duration of 35 ms at all thethree response locations. A typical plot is shown in Fig. 6 for all three locations ofmeasurement.

6 Observation from the Horizontal Test

The horizontal tests were performed following similar procedure. However, theresponse from the three locations showed wide variation in amplitude of the pulseand its duration. As the test vessel is unsymmetrical in horizontal position, a counterweight at the bottom end (non-flanged end) was provided to balance its horizontalfall. A balancing weight was placed on the supporting frame as shown in Fig. 3.

Under this condition, the shock experienced by the three locations had widevariations [10] as shown in first few rows of Table 2 (trials 1–3). Figure 7 showstypical plots from horizontal tests of the vessel with the balance weight for the three

Table 1 Vertical test trials

Trialno.

Dropheight(mt)

Sensorlocation

Unfiltered Filtered

Pulse amp.level (g)

Pulsetime (ms)

Pulse amplitudelevel (g)

Pulsetime (ms)

1 0.35 1 22 35 19 35

2 27 35 20 35

3 22 35 21 35

2 0.38 1 23 35 20 38

2 27 35 22 38

3 22 35 22 38

3 0.45 1 25 30 23 38

2 31 30 23 38

3 25 30 24 35

4 0.5 1 27 35 24 40

2 31 35 24 40

3 28 35 24 40

5 0.5 1 28 35 24 35

2 32 35 26 35

3 28 35 26.5 35

6 0.5 1 28 35 23.5 36

2 31 35 25 35

3 26 35 26 35

For sensor location see Fig. 2


locations for 0.28 m drop height and 17 layers of rubber pads in two stacks close tothe center. The shock amplitudes at the ends were high as compared to shock in thecentre. The pulse showed a double peak feature as shown in Fig. 8, which is adistorted shape of half sine shape. It also had longer pulse duration.

The assembly was then made to fall on four stacks of rubber pads. Due todifferent contact time of different portions of the assembly on the rubber pads andthe shock traversal from ends towards the centre, variation in the shock amplitudeshowed more distortions. So, this scheme was not pursued further.

The assembly was then made to fall on two decks of rubber pads positionedfurther close to the centre for a uniform fall and response. Though the double peakfeature at the centre improved to a single peak like pattern, the pulse duration wasvery long with reduced peak acceleration levels. Shock amplitudes at the ends werevery high as compared to in the centre as shown in Table 2 (trials 7–8). The reasonwas recoil motion of the overhung end portion. Some typical plots are shown inFigs. 7 and 8 for the horizontal test with balance weight and two decks of rubberpads with various arrangements.

For better symmetry in mass distribution, a counter flange was fitted to thebottom end of the vessel instead of the counter weight tried earlier on the supportingstructure. To minimize the distortion at the middle and at the end, the assembly was

Table 2 Horizontal test trials

Trialno.

Dropheight(mt)

Sensorlocation

Unfiltered Filtered

PulseAmplitudeLevel (g)

PulseTime(ms)

PulseAmplitudeLevel (g)

PulseTime(ms)

1 0.25 1 32 30 29 32

2 25 33 19 33

3 25 25 24 25

2 0.28 1 31 33 28 35

2 26 35 19.5 35

3 25 30 23 35

3 0.3 1 36 25 35 30

2 22 25 19 30

3 38 20 35 32

4 0.35 1 38 28 36 30

2 25 30 23 35

3 40 30 38 30

5 0.35 1 37 30 35 32

2 25 25 22 30

3 40 30 37 30

For sensor locations, refer Figs. 3 and 4


made to fall on two stacks of rubber pads instead of four (which showed moredistortion in the response) for the horizontal tests. The two ends of vessel recordedhigher ‘g’ level of shock pulse duration, where as the middle showed lower ‘g’ andlonger pulse. To maintain the minimum required ‘g’ level throughout, the heightand drop targets were adjusted. However, the level shown by the end responseswere always more than the required level.

By repeated adjustment of drop height and the position of the target, the shocklevels were brought to acceptable value as shown in Fig. 9 and in Table 2 (trials9–10).

s4.71 4.72 4.73 4.74 4.75 4.76

kg

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

C:(0.00000 s, 0.00259 kg) Recorded Wave File Ch. 1

s4.71 4.72 4.73 4.74 4.75 4.76

kg

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03


35 msec

32 g

s4.715 4.720 4.725 4.730 4.735 4.740 4.745 4.750 4.755

kg

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03


35 msec

(a) (b)

(c)(d)

(e) (f)

25 g

Fig. 6 Vertical drop test with 13 layers of rubber pads and 0.5 m drop height (trial 5, Table 1; a, c,e unfiltered signal, b, d, f filtered signal), x-axis → time and y-axis → acceleration in g.a Response from bottom (unfiltered). b Response from bottom (filtered). c Response from middlelange (unfiltered). c Response from middle lange (unfiltered). e Response from top flange(unfiltered). f Response from top flange (filtered)


7 Analysis

The signals were analyzed with a standard analyzer and the data were recorded forfurther conditioning. The raw signals normally consist of high frequency contentsin the form of spikes [10]. The high frequency noises were filtered out usingMATLAB to arrive at the decisive pulse.

The drop height and number of targets to be used in horizontal test was arrived atby several adjustments. The repeatability of the tests was performed to confirm their

s3.89 3.90 3.91 3.92 3.93 3.94 3.95

kg

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03


s3.90 3.91 3.92 3.93 3.94 3.95

kg

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03


s3.905 3.910 3.915 3.920 3.925 3.930 3.935 3.940 3.945

kg

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03


(a) (b)

(c) (d)

(e) (f)

Fig. 7 Horizontal drop test of the vessel with balance weight with 17 layers of rubber pads in twodecks located near the centre and 0.28 mt drop height (Trial 2, Table 2). (a, c, e unfiltered signaland b, d, f filtered signal). a Response from top (unfiltered). b Response from top (filtered).c Response from middle (unfiltered). c Response from middle (unfiltered). e Response from bottom(unfiltered). f Response from bottom (filtered)


s10.79 10.80 10.81 10.82 10.83 10.84

kg

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03


(a) (b)

Fig. 8 Typical time spectra showing double peak feature of the response at the middle flange(with balance weight). a Horizontal test (unfiltered) shock at middle flange with drop height 0.35mt and 17 layers of target pads. b Horizontal test (filtered) shock at middle flange with drop height0.35 m and 17 layers of target pads

s10.775 10.780 10.785 10.790 10.795 10.800 10.805

kg

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04


s11.160 11.165 11.170 11.175 11.180 11.185 11.190 11.195 11.200

kg

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03


(a) (b)

(c) (d)

Fig. 9 Typical shock pulses for the horizontal test of the assembly from sensor 1 and 2 of the testvessel with the balancing flange at the bottom (other end). (a, c, e unfiltered signal and b, d,f filtered signal). a Horizontal test (unfiltered) (height 0.3 mt, 17 layers sensor 1). b Horizontal test(filtered) (height 0.3 mt, 17 layers pad, sensor 1). c Horizontal test (unfiltered) (height 0.35 mt, 17layers pad, sensor 2). d Horizontal test (filtered) (height 0.35 mt, 17 layers pad, sensor 2)


reproducibility. Though the results of vertical tests were acceptable, the horizontaltests showed wide variations as regard to the pulse amplitude and duration for thethree locations. Owing to the huge horizontal span, the levels were difficult to adjustto a uniform level at all the locations. However, efforts were made to make the levelsuch that, 25 g acceleration is measured on the vessel with reasonable time durationin all the portions.

8 Analysis for Shock Response Spectrum (SRS)

Shock response spectrum [13] is a plot of the maximum response to a specifiedshock load for all possible single degree of freedom systems in the frequency rangeof consideration. This is a useful tool in analyzing systems for design qualification,especially for seismic loading.

Analytical approach was followed to ensure that the achieved shock levelenvelopes the response spectrum of the desired shock at least up to the desiredfrequency range. A typical shock response spectrum (SRS) for the ideal shock levelof 25 g and 35 ms duration is shown in Fig. 10. The analyzed SRS is up to 250 Hzfor single degree of freedom systems having a viscous damping ratio of 10 %. Thebehavior will be similar for any other damping value. Figure 11 shows theenveloping trend of the SRS of a 26 g–34 ms shock pulse. Though both the SRStrends look similar up to 15 Hz, the 26 g–34 ms SRS clearly overshoots the idealSRS beyond 15 Hz. To prevent under qualification, the achieved SRS shouldenvelope the ideal SRS in the desired frequency range. Similar analysis was donefor all the achieved shock levels.

Fig. 10 Shock responsespectrum for 25 g and 35 msshock pulse with a systemdamping ratio of 10 %


9 Conclusion

(a) Shock testing using the drop test method may show inconsistencies as regardto the level and duration of the shock pulse, when seen from different responselocations on the test specimen especially when the test structure is large.

(b) Several response locations on the test piece are advised, as the reflection fromone location may not be the actual representation of the whole structure.

(c) Test specimen undergoing restricted number of shock cycles during test, needspecial care in standardizing the test procedure for shock level and durationprior to subjecting the specimen for actual test.

(d) The drop height, ground condition and the drop target are sensitive parametersto control and standardize the procedure. They need validation from time totime to account for the changing conditions during the tests.

(e) Normally, the increase in drop target thickness (rubber pads) was found toincrease the time duration of pulse and an increase in drop height increases theshock level.

(f) Any change in shape and size of the specimen need validation of the dropheight and target.

(g) Consistent reproducibility is important and need constant vigilance to avoidunder or over qualification of part or whole of the structure.

(h) If the noisy signal is not properly handled by appropriate filtering technique,getting to acceptable level and duration of shock may be difficult even forstraight forward tests like in vertical direction.

SRS trend of the 26g -34 msec shock pulse

SRS trend of the ideal shock pulse

Fig. 11 Shock responsespectrum for a shock load of26 g and 34 ms time showingenveloping of the ideal SRS


References

1. ASME (2010) Boiler and pressure vessel code, Section I, IV, III, XI, VIII, X, XII2. ISO 4866:2010—Mechanical vibration and shock—vibration of fixed structures—guidelines

for the measurement of vibrations and evaluation of their effects on structures3. ISO 18431:2007—Mechanical vibration and shock—signal processing—Part 4: Shock-

response spectrum analysis4. Harris CM, Peirsol AG (2001) Shock and vibration handbook, 5th edn. McGraw Hill, New

York5. ICC-ES AC156, Seismic qualification by shake-table testing of nonstructural components and

systems. www.icc-es.org/criteria/pdf_files/ac156.pdf6. Rittweger A, Beuchel W, Andersen MG, Albus J (2005) Lessons learned from the dynamic

identification/qualification tests on the ESC-A upper stage model. Acta Astronaut 57(12):877–886

7. Meher KK, Rao AR (2006) Optimization of the number of spacers in a nuclear fuel bundlewith respect to flow-induced vibration. Nucl Eng Des 236(22):2348–2355

8. Moorthy RIK, Sinha JK (1998) Dynamic qualification of complex structural components ofnuclear power plants. Nucl Eng Des 180(2):147–154

9. Bertram A (1980) Dynamic qualification of large space structures by means of modal couplingtechniques. Acta Astronaut 7(10):1179–1190

10. Meher KK, Narayan AK, RamaRao A (2010) Drop test of assembly with CCG and PCG,RED/VLS/2010, dated Jan 27, 2010. BARC internal report

11. Meher KK, Narayan AK, RamaRao A (2010) Re-calibration of K-200 shock testing machine.RED/DS/VLS/2010/567, dated Feb 25, 2010, BARC internal report

12. Theory of vibration/shock isolators, www.rpmmech.com/pdf/selecting-a-vibration-shock-isolator.pdf

13. Thomson WT, Dillon Dahleh M (2005) Theory of vibration with applications, 5th edn.Pearson Education, Singapore


http://www.icc-es.org/criteria/pdf_files/ac156.pdf

http://www.rpmmech.com/pdf/selecting-a-vibration-shock-isolator.pdf

http://www.rpmmech.com/pdf/selecting-a-vibration-shock-isolator.pdf

Documents

[Mechanisms and Machine Science] Vibration Engineering and Technology of Machinery Volume 23 || Qualification of Large Structures for Shock Loads