Design and analysis of shock and random The Author(s) 2013 ...ashkanhh.mit.edu/sites/default/files/images/JVC1.pdf · ATR chassis including two jet impingement chambers is modeled

Article

Design and analysis of shock and randomvibration isolation system for a discretemodel of submerged jet impingementcooling system

Ashkan Haji Hosseinloo, Fook Fah Yap and Liang Ying Lim

Abstract

High-powered embedded computing equipment using air transport rack (ATR) form-factors are playing an ever-increas-

ing role in critical military applications in air, land and sea environments. High power and wattage of the electronics and

processors require large heat dissipation, and thus more sophisticated and efficient thermal cooling systems such as loop

heat pipes or jet impingement systems are demanded. However, these thermal solutions are more susceptible to harsh

military environments and thus, for proper performance of thermal and electronic equipment, they need to be protected

against shock and vibration inherent in harsh environments like those in military applications. In this paper, an isolated

ATR chassis including two jet impingement chambers is modeled as a three-degrees-of-freedom system and its response

to random vibration and shock has been studied. Both finite element and experimental modal analysis is utilized to

characterize dynamics of the components of the jet impingement system. The response of the model is compared to that

of the traditional single-degree-of-freedom model, and the isolation system is optimized in terms of its damping.

Keywords

Discrete model, jet impingement, modal analysis, random vibration, shock, vibration isolation

1. Introduction

As the trend of highly integrated electronics and simul-taneous miniaturization escalates to include faster pro-cessors, more functions, and higher bandwidths,electronics continue to become more compact inresponse to size limitations and strict reliability require-ments (Ohadi and Jianwei, 2004). The result is anincreasing heat flux at both the component and circuitboard levels. Limited power dissipation with someother pitfalls of convection and conduction coolingmethods are pushing towards exotic techniques suchas liquid-cooling and spray-cooling systems. Thesemethods can provide higher heat dissipation powerand can be used in rugged environments like in fightersor ground mobile vehicles if they are made ruggedaccordingly.

A jet impingement cooling system is a relatively newcooling technology that is nowadays being given ser-ious consideration in high power electronics coolingsystems. In this cooling system working fluid, which isusually water, is pumped into a chamber and is then

pushed through tiny nozzles drilled into a so-callednozzle plate. On the other side of the nozzle plate, thehigh velocity water jets impinge on the heat sourcessuch as circuit boards either directly or through anintermediate plate called an impingement plate that ismounted back to back to the heat sources. Thus, theheat is dissipated and water is drained to a heat rejec-tion unit (HRU) such as a radiator to reject the heatfrom the water, and it is then pumped back to thechamber to repeat the closed loop. In this project,two impingement units are used to dissipate a totalpower of 2 kW from two circuit boards (1 kW each).

School of Mechanical and Aerospace Engineering, Nanyang Technological

University, Singapore

Corresponding author:

Ashkan Haji Hosseinloo, School of Mechanical and Aerospace

Engineering, Nanyang Technological University, 50 Nanyang Avenue,

639798, Singapore.

Email: [email protected]

Received: 15 March 2013; accepted: 11 April 2013

Journal of Vibration and Control

2015, Vol. 21(3) 468–482

! The Author(s) 2013

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DOI: 10.1177/1077546313490186

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A CAD model of the impingement system is illustratedin Figure 1, and the thermal diagram of the coolingsystem is depicted in Figure 2. In the latter diagramthe AC power is used to provide the required wattagefor the heaters, and the data acquisition unit is used tocapture the temperature of the thermocouples mountedin the impingement plates to assess the performance ofthe cooling system.

Two units of the cooling system shown in Figure 1together with their attached heating sources aremounted in an ATR using wedge locks. The wholeATR chassis is subjected to severe random vibrationand shock. The heat rejection unit is placed outsidethe chassis and is not subjected to shock and vibration.The goal in this project is to protect the cooling systemrather than the heating sources (which could be printedcircuit boards or some other heat sources) againstshock and vibration. A common practice to ruggedizeand protect sensitive devices against shock and vibra-tion is either to stiffen them, which adds to the totalmass and volume and is not always practical, or toisolate them from the base excitations. The traditionaloptimal design for vibration isolation from randomvibration is based on a trade-off choice of dampingand stiffness properties of mounts, and is focused pri-marily on optimizing the dynamic response of the entireenclosure or chassis, subject to limitations imposed ontheir rattle space (Veprik, 2003). However, somedevices include lightly damped components that arehighly responsive to a wide range of frequencieswhich are not considered in the traditional isolation

system design. Consequently, traditionally designedisolation systems ignoring the responsive internal com-ponents are insufficient for maintaining a fail-safevibration environment for the system.

Although the traditional design may fulfill the shockor vibration requirements in some applications (Allenet al., 2000; Yap et al., 2006; Harmoko et al., 2009; Ohet al., 2012; Baril et al., 2012), it does not always resultin an optimum design. Therefore, the traditional trendof isolators’ design has been challenged in the lastdecade in certain areas such as printed circuit boards,cryogenic coolers and hard disk drives. Veprik andBabitsky (2000) added a secondary degree of freedom(d.f.) for a printed circuit board to the model of anisolated rigid electronic box and tried to optimize theisolator’s parameters for a harmonic excitation to min-imize the PCB’s absolute acceleration or relative deflec-tion, subject to an overall rattle space of the box. Later,Veprik (2003) used the same model to optimize the iso-lator’s properties this time for random vibration input.

Veprik and his colleagues (2001) designed an isola-tion system for an infrared equipment to minimize thevibration-induced line-of-sight jitter which was causedby the relative deflection of the infrared sensor and theoptic system. They added a second d.f. for the coldfinger of the cryogenic cooler to the main single-d.f.model of the system to improve the model as a morerealistic two-d.f. system. Later on, they used this two-d.f. model which included the sensitive cantileveredcold finger to design optimum compliant snubbers forimpact protection (Veprik et al., 2008).

Figure 1. (a) Exploded view of the assembly of the jet impingement system; chamber housing, nozzle plate, and impingement plate

(from top to bottom); (b) assembled jet impingement chamber.

Hosseinloo et al. 469



Jet impingement systems include dynamically sensi-tive components that could be very responsive to highfrequency excitations. As mentioned earlier, the needfor use of these cooling systems in harsh militaryenvironments is now increasing more than ever,hence calls for systematic shock and vibration protec-tion analysis which is not available at the time. Theauthors previously designed an integrated linear-non-linear vibration isolation system for the ATR chassismentioned above catering for base random vibrationinput in the presence and absence of g-loading(Hosseinloo and Yap, 2011). However, their modelignored the presence of internal components. In thisarticle, the authors optimize a linear isolation systemfor shock and random vibration inputs considering thesensitive internal components of the impingementsystem.

2. Mathematical modeling

2.1. Traditional Single-degree-of-freedom modelof the isolated system

A traditional single-d.f. model of the isolated system isshown in Figure 3, where the chassis and the includedtwo cooling chambers and two micro pumps are mod-eled as a single rigid object with mass m. Isolator stiff-ness and damping are designated by kc and cc.

Using random vibration theory (Newland, 1996) andtransmissibility functions for an single-d.f. model,

variance of absolute acceleration of the chassis and itsrelative deflection are found as, respectively:

�2€x ¼Z10

S €xb ð j!Þ Tabsð j!Þ�� 2d!

¼Z10

S €xbð j!Þð!2c þ 2j!!c�cÞ

ð!2c � !2 þ 2j!!c�cÞ

��2

d!

ð1Þ

Figure 2. Thermal diagram of the jet impingement cooling system.

Figure 3. Single-degree-of-freedom model of the chassis with

the cooling system.

470 Journal of Vibration and Control 21(3)



and

�2z ¼Z10

S €xbð j!Þ!4

Trelð j!Þ�� 2d!¼ Z

1

0

S €xbð j!Þ!2c �!2þ 2j!!c�c�� 2d!

ð2Þ

where z is the chassis relative displacement(z ¼ xc � xb), and S €xb is the base one-sided power spec-tral density. Conventional notation is used for naturalundamped frequency (!c) and damping ratio (�c) asbelow,

!c ¼ffiffiffiffik

m

rand �c ¼

c

2ffiffiffiffiffiffiffikmp ð3Þ

The base excitation is Gaussian random excitationwith zero mean value. Thus, as the system is linear, theresponse will also be Gaussian with zero mean thatconsequently allows us to use the 3s rule to estimatethe maximum vibration travel of the chassis as

zpeak ¼ 3�z ð4Þ

Fatigue damage accumulation of sensitive compo-nents depends mainly on the transmitted absolute accel-eration (Ho et al., 2003); hence, to assess and quantifythe quality of vibration isolation a parameter calledattenuation factor (AF) is introduced and defined asthe root mean square (RMS) value of the absoluteacceleration of the hard mounted chassis divided bythat of the isolated chassis as follows:

AF ¼ � €xb� €x

ð5Þ

Finally, the shock response of the chassis is obtainedby solving the following dynamic equation:

€zþ 2�c!c _zþ !2c�c ¼ €xb ð6Þ

2.2. Proposed three-degree-of-freedom model ofthe isolated system

The chassis is quite stiff and could be considered rigidfor the frequency range of the excitation considered inthis article, i.e. 20Hz to 2000Hz. There are two I-driveIEG micro pumps in the chassis that apply quite smallharmonic forces to the chassis and are considered neg-ligible. However, the three components of the impinge-ment cooling system mentioned earlier could be flexibleto the excitation normal to the impingement and nozzleplates. To check if the three components – namely,chamber housing, nozzle plate and impingement

plate – have responsive modes to the random basevibration ranging from 20Hz to 2000Hz, modal ana-lysis of the components is conducted in ANSYS. Forthe modal analysis both the chamber housing and theimpingement plate have been fully constrained at theirmounting holes. Table 1 shows the first six undampednatural frequencies of the chamber housing andimpingement plate, and Figure 4 illustrates the corres-ponding mode shapes of these natural frequencies forthe two components.

A rule of thumb in modal analysis states that allfrequencies below one-and-a-half times the maximumexcitation frequency should be considered for dynamicanalysis. According to the modal analysis, the first nat-ural frequency of the chamber housing is well above3000Hz and it can be considered rigid. The impinge-ment plate is quite flexible in the excitation frequencyrange; however, this plate is mounted back to back to athick copper heating plate (Figure 5) that both togethercan be considered rigid. According to the modal ana-lysis of the impingement plate, if a heating source withrelatively negligible flexural rigidity is used, the flexibil-ity of the impingement plate should be considered.

The nozzle plate has 285 tiny nozzles with diameterof 0.5mm which makes the element size in the finiteelement (FE) meshing very small, and hence increasesthe number of elements and the computational timesignificantly. To check if the nozzles have a consider-able effect on the modal analysis of the plate, two quar-ter nozzle plates with symmetric boundary conditionshave been modeled; one with and the other withoutnozzle holes, and their first few frequencies have beencompared in Table 2. According to the table, nozzleholes have no significant effect on the modal analysis,and thus nozzle plate without nozzles is used for themodal analysis. The first six natural frequencies of thenozzle plate and the corresponding mode shapes aregiven by Table 1 and Figure 6, respectively.

According to Table 1 the nozzle plate has its firstnatural frequency below 3000Hz, hence it should beconsidered in the dynamics of the problem. Sincethere is only one responsive mode for the excitationfrequency range considered here, the nozzle plate

Table 1. The first six natural frequencies of the three compo-

nents of the cooling chamber.

Mode number

Natural frequency (Hz)

1 2 3 4 5 6

Chamber housing 4395 7801 9364 12618 12991 15773

Impingement plate 935 1583 2176 2643 2772 3773

Nozzle plate 2763 4983 5027 7854 9022 7942




could be modeled as an additional single-d.f. system.There is another assumption made in this analysisregarding the water effect on the dynamics of thesystem. Because there is a constant water pressure dif-ference between the two sides of the nozzle plate, itcould reasonably be assumed that the water affectsthe plate by giving it a negligible small initial deflection

and will also add some viscous damping to the systemthat is ignored in this article.

Having considered the assumptions, a three-d.f.model of the system could be represented as shown inFigure 7. Since the two nozzle plates are identical thethree-d.f. model could be further reduced to a two-d.f.one to simplify the system dynamics.

Figure 4. The first six mode shapes of the chamber housing and impingement plate.

Figure 5. The cooling chamber attached to the heating copper block and Teflon insulation plate.




In the proposed model the damping and effectivemass of the nozzle plate are still unknown and theyare found using an impact hammer test. The hammertest set-up is shown in Figure 8. The fixture is designedso as to resemble the actual boundary conditions. Asonly the first mode of the nozzle plate is of interest, thenozzle plate is hit at its center and the acceleration isread at the same point at the other side of the plate.Figure 9 shows the point accelerance frequencyresponse function (FRF) of the nozzle plate. Anembedded nonlinear least square curve fitting tool inMATLAB is used to curve fit the experimental accel-erance of the plate with analytical accelerance equation

Figure 6. The first six mode shapes of the nozzle plate.

Table 2. Comparison between natural frequencies of the

quarter nozzle plates with and without nozzles.

Mode

number

Natural frequency (Hz)

Discrepancy

percentage %

With

nozzles Without nozzles

1 2752.5 2762.7 0.37

2 7759.8 7786.2 0.34

3 8945.4 8979.8 0.38

4 13306 13316 0.075

5 14433 14482 0.34




Figure 8. Impact hammer test setup for modal identification of the nozzle plate.

Figure 7. Three-degrees-of-freedom model of the isolated chassis and the cooling system.




of an single-d.f. model. The curve fitted parameters,namely the effective mass (mn), natural frequency (!n)and damping ratio (�n) of the first mode of the nozzleplate are found as 0.025 kg, 3003Hz, and 3.7%, respect-ively. The 8% discrepancy between the natural frequen-cies obtained from FE and experimental analysis forthe first mode is mainly due to the difference betweenthe actual boundary condition and the simplified oneused in FE modal analysis. With the above extractedeffective mass, the nozzle plate mass ratio (m) will beabout 0.0015.

After parameter identification through FE andexperimental modal analysis, and modeling thesystem, dynamic equations of the system can bederived. Complex transmissibility of the absolute accel-eration of the nozzle plate is derived as

TR €xn€xbðsÞ ¼ TRxnxbðsÞ ¼

€XnðsÞ€XbðsÞ¼ XnðsÞ

XbðsÞ

¼ ð2�n!nsþ !2nÞ

ðs2 þ 2�n!nsþ !2nÞTRxcxbðsÞ,

ð7Þ

where TRxcxb ðsÞ is complex transmissibility of the abso-lute acceleration of the chassis,

In the equations above, conventional notation hasbeen used as follows:

!2n ¼knmn

, !2c ¼kcmc

, �c ¼cc

2ffiffiffiffiffiffiffiffiffiffikcmcp , �n ¼

cn

2ffiffiffiffiffiffiffiffiffiffiffiknmnp

and � ¼ mnmc

ð9Þ

Furthermore, the complex transmissibility functionsof the chassis rattle space and the nozzle plate deflec-tion can be obtained as

TRz1€xb ðsÞ ¼ TRxc�xb€xbðsÞ ¼ XcðsÞ � XbðsÞ

€XbðsÞ

¼ XcðsÞ � XbðsÞs2XbðsÞ

¼ 1s2

TRxcxb ðsÞ � 1� � ð10Þ

and

TRz2€xbðsÞ ¼ TRxn�xc€xbðsÞ ¼ XnðsÞ � XcðsÞ

€XbðsÞ

¼ XnðsÞ � XcðsÞs2XbðsÞ

¼ 1s2

TRxnxbðsÞ � TRxcxbðsÞ

� �ð11Þ

TR €xc€xbðsÞ ¼ TRxcxbðsÞ ¼

€XcðsÞ€XbðsÞ¼ XcðsÞ

XbðsÞ

¼ ðs2 þ 2�n!nsþ !2nÞð2�c!csþ !2cÞ

ðs2 þ 2�n!nsþ !2nÞ s2 þ ð2�c!c þ 4��n!nÞsþ !2c þ 2�!2n� �

� 2�ð2�n!nsþ !2nÞ2

ð8Þ

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

50

100

150

200

250

300

350

400

450

500

frequency (Hz)

Acc

eler

ance

(m

s−2 /

N)

Experimental dataSDOF curve fit

Figure 9. Experimental and fitted theoretical single-degree-of-freedom accelerance curves.




According to the last two equations the chassisvibration travel and the nozzle plate deflection aredesignated as z1 and z2. Having derived the transmissi-bility functions, RMS absolute acceleration of thenozzle plate can be calculated as

� €xn ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZþ10

S €xnð!Þd!

vuuut ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZþ10

TRxcxb ð j!Þ�� 2S €xb ð!Þd!

vuuutð12Þ

The maximum nozzle plate deflection and chassisvibration travel can also be evaluated using the 3srule as follows, respectively:

zpeak2 ¼ 3�z2 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZþ10

Sz2 ð!Þd!

vuuut

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZþ10

TRz2€xbð j!Þ�� 2S €xb ð!Þd!

vuuut ð13Þand

zpeak1 ¼ 3�z1 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZþ10

Sz1 ð!Þd!

vuuut

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZþ10

TRz1€xbð j!Þ�� 2S €xbð!Þd!

vuuut ð14ÞFor a meaningful definition, attenuation factor for

the three-d.f. system is defined as

AF ¼� €xn��!c!þ1� €xn

ð15Þ

After defining and formulating the attenuationfactor and relative deflections, the optimization prob-lem should be defined and formulated as well; the prob-lem is to find !c and �c such that €xn and z2 areminimized, subject to a maximum rattle space:z1 � �max where �max is the maximum allowed vibra-tion travel of the chassis.

Regarding the problem definition, one should notethat:

(i) Minimization of €xn is important for fatigue andcatastrophic failure of the nozzle plate.Acceleration of the nozzle plate may also affectthe impingement mechanism.

(ii) Minimization of z2 is important for thermal per-formance of the cooling system. z2 is a measure ofchange in impingement height (the clearance

between the nozzle plate and the impingement sur-face), which directly affects the coolingperformance.

(iii) Rattle space and vibration travel constraint isimportant because the system should be finallyconfined within a specified volume.

In addition to random base excitation, response ofthe system to base shock excitation should also be ana-lyzed. As mentioned earlier, since the two d.f. pertain-ing to the two nozzle plates are identical, dynamicequations of motion can be reduced from three totwo, and be formulated in the matrix form as follows:

€zþ C_zþ Kz ¼ r €xb ð16Þ

where

z¼ ½ z1 z3 �T,K¼!2c þ 2�!2n �2�!2n�!2n !2n

" #,

r¼ ½�1 �1 �T, and C¼2�c!cþ 4��n!n �4��n!n�2�n!n 2�n!n

� :

ð17Þ

In the above equation, z3 is deflection of the nozzleplate relative to the base (z3 ¼ xn � xb).

Having derived the equations of motion of the twosystems, the response of the single-d.f. and three-d.f.models to shock and random vibration inputs will bepresented in the following section.

3. Results and discussion

The random vibration excitation considered in this art-icle is an ergodic and stationary random vibration withpower spectral density (PSD) shown in Figure 10(a).The vertical axis of the figure is in decibels and inunits of (g2/Hz). The flat part of the profile correspondsto a PSD level of 0.50 g2/Hz. The corresponding overallRMS value of the base acceleration is about 31grms.The shock excitation considered here is an end-termi-nating sawtooth shock with duration of 11ms and max-imum acceleration of 20 g (Figure10(b)).

Figure 11 shows dependency of the attenuationfactor on damping ratio for a few isolation frequencies.According to the figure, attenuation factor decreaseswith an increase of the isolation frequency for any iso-lation damping ratio; however, there is an optimumdamping ratio that maximizes the attenuation factorat the nozzle plate for a given isolation frequency.The optimum damping ratio varies from 0.17 to 0.31for isolation frequency range of [20,50] Hz. Althoughthe optimum damping ratios for a given isolation fre-quency are almost the same for the two models, the




corresponding attenuation factors are quite different.This is because the nozzle plate in the three-d.f.model works as a secondary vibration isolation andreduces the transmitted acceleration at its center (firstmode). For instance, attenuation factor at the nozzleplate at an isolation frequency of 20Hz with corres-ponding optimum damping ratio of 0.17, is about29.3 using the three-d.f. model, that is, 23% largerthan that of the single-d.f. model, i.e. 23.8.

For a given isolation frequency, as the isolationdamping increases maximum isolator deflection (chas-sis vibration travel or rattle space) decreases; however,this value for any given damping ratio is maximized atan isolation frequency of about 22Hz. This is becauseof the resonance of the isolation system at the begin-ning of the base excitation frequency; lower excitationfrequencies result in higher displacements. Figure 12shows how vibration travel of the chassis varies with

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

ωc=20Hz

ωc=30Hz

ωc=40Hz

ωc=50Hz

isolation damping ratio

atte

nuat

ion

fact

or

ωc=20Hz

ωc=30Hz

ωc=40Hz

ωc=50Hz

SDOF model3DOF model

Figure 11. Dependency of attenuation factor on isolation damping ratio at different isolation natural frequencies.

0 2 4 6 8 10 12 140

5

10

15

20

time (ms)

8 16 32 64 128 256 512 1024 2048 4096

-18

-16

-14

-12

-10

-8

-6

-4

-2

Frequency (Hz)

6dB/octave

(a) (b)

Figure 10. (a) Power spectral density profile of the base random acceleration; (b) end-terminating sawtooth shock profile of the

base.




isolation frequency at a given damping ratio.According to the figure, there is not much differencebetween the responses of the two models in terms ofthe chassis vibration travel. The reason is that thenozzle plate mass ratio is so small (m¼ 0.0015) thatthe nozzle plate’s dynamics will not have a significanteffect on the dynamics of the rest of the system.

A pitfall of the single-d.f. model is that it is incapableof giving any information about the nozzle plate deflec-tion; however, in view of the three-d.f. model this infor-mation can be evaluated. Nozzle plate deflection isimportant as it affects the impingement height that con-sequently affects the thermal performance of theimpingement system. It is desirable that the variationin impingement height is minimal. Figure 13 depictshow maximum deflection of the nozzle plate (changein the impingement height) varies with isolation damp-ing ratio for different isolation frequencies. Accordingto the figure, for a given isolation frequency there is anoptimum damping ratio that minimizes the change inimpingement height. This optimum damping value isthe same damping that maximized the attenuationfactor shown in Figure 11. This is because the fre-quency response function of the nozzle plate’s deflec-tion is the same as that of the plate’s accelerationdivided by the frequency squared. Because the powerspectral density is a product of the input power spectraldensity and square of the FRF magnitude, PSD ofthe nozzle plate’s deflection will be the same as thatof the plate’s acceleration divided by a frequency to

power of four. This consequently results in the sameoptimum damping minimizing the plate’s accelerationand deflection.

Figure 14 depicts the shock response spectrum ofthe normalized absolute acceleration of the nozzleplate for the two models. Acceleration is normalizedby the maximum input shock, i.e. 20 g. According tothe figure there is not much difference between the twomodels’ responses for the shock input, and that isbecause frequency contents of the shock are notclose enough to the nozzle plate’s first natural fre-quency. Figure 15 shows normalized maximum abso-lute acceleration of the nozzle plate as a function ofisolation damping ratio at different isolation frequen-cies for the two models. For the single-d.f. model inFigures 14 and 15 the acceleration of the chassis istaken as the acceleration of the nozzle plate.According to Figure 15 there is an optimum dampingratio for isolation natural frequencies below 40Hz thatminimizes the maximum acceleration transmitted tothe nozzle plate. This optimum damping ratio isabout 0.25 for isolation frequencies ranging from10Hz to 40Hz.

Just like the random vibration input, the maximumisolator’s deflection is analyzed for the shock input. Theisolator’s deflection is important as it gives informationabout meeting the rattle space requirement and aboutthe possibility of bottoming out if it is above the max-imum allowed stroke of the isolator. Figure 16 showsthe shock response spectra of the isolator’s deflection

0 10 20 30 40 50 60 70 80 90 1000.5

1

1.5

2

2.5

3

3.5

4

4.5

isolation natural frequency(Hz)

max

imum

def

lect

ion(

mm

) ζc=0.05

ζc=0.1

ζc=0.2

ζc=0.3

ζc=0.4


Figure 12. Dependency of isolator’s maximum deflection on isolation natural frequency at different isolation damping ratios.




for the two single-d.f. and three-d.f. models. Accordingto the figure, there is not much difference between theresponses of the two models to the shock excitation andthe reason lies again in the fact that the nozzle plate

mass ratio to the rest of the system is too small to affectthe dynamics of the chassis.

As mentioned earlier, the three-d.f. model enables usto look at maximum deflection of the nozzle plate while

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 10

−3

ωc=20Hz

ωc=30Hz

ωc=40Hz

ωc=50Hz


max

imum

def

lect

ion(

mm

)

Figure 13. Maximum deflection of the nozzle plate versus isolation damping ratio at different isolation frequencies.

0 50 100 150 200 250 3000

0.2

0.4

0.6

0.8

1

1.2

1.4

isolation natural frequency (Hz)

norm

aliz

ed a

bsol

ute

acce

lera

tion


ζc=0.05 ζc=0.1

ζc=0.2

ζc=0.4

ζc=0.3

Figure 14. Normalized absolute acceleration shock response spectrum of the nozzle plate for the single-degree-of-freedom and the

three-degrees-of-freedom models.




the single-d.f. model is incapable of giving this infor-mation. Figure 17 shows maximum deflection of thenozzle plate as a function of isolation damping ratioat different isolation natural frequencies for the three-

d.f. model. According to the figure there is an optimumdamping ratio for isolation natural frequencies lowerthan 40Hz that minimizes the nozzle plate’s maximumdeflection. Similar to the random excitation input, this

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2


norm

aliz

ed m

axim

um a

ccel

erat

ion

ωc=10Hz

ωc=20Hz

ωc=30Hz

ωc=40Hz


Figure 15. Normalized maximum absolute acceleration of the nozzle plate versus isolation damping ratio at different isolation

natural frequencies for the two single-degree-of-freedom and the three-degrees-of-freedom models.

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25

30

isolation natural frequency (Hz)

max

imum

def

lect

ion

(mm

)


increasing damping ratio(ζ)ζ

c=0.05, 0.1, 0.2, 0.3, 0.4

Figure 16. Isolator’s deflection shock response spectrum for the single-degree-of-freedom and the three-degrees-of-freedom

models.




optimum damping ratio is equal to the dampingratio that minimizes the nozzle plate’s maximum accel-eration when subjected to the shock, i.e. a dampingratio of 0.25.

4. Conclusion

In this article random vibration and shock protectionof submerged jet impingement cooling systems havebeen investigated and compared with traditional rug-gedization methods. Unlike traditional methods thecurrent research aims at reducing the transmitted vibra-tion to internal critical components of the impingementsystem. FE and experimental modal analysis are con-ducted to characterize different components of the cool-ing system; hence, a three-d.f. model of the isolatedsystem is proposed that has an addition of two d.f.for the nozzle plates as compared to the traditionalsingle-d.f. model. The problem is defined as to findoptimum isolator properties to minimize the nozzleplates’ acceleration and deflection while the whole chas-sis containing the impingement system is confinedwithin an allowed rattle space.

The results show that there is a considerable differ-ence between the calculated acceleration of the nozzleplate using the single-d.f. and three-d.f. models.Furthermore, the three-d.f. model enables us to calcu-late the nozzle plate’s deflection, which is important for

the impingement cooling system performance.According to the results, for random base excitationthere is an optimum damping ratio minimizing boththe nozzle plate acceleration and deflection that variesfrom 0.17 to 0.31 for an undamped isolation frequencyrange of [20,50] Hz. Furthermore, there is an optimumisolation damping ratio of 0.25 for isolation frequenciesbelow 40Hz that minimizes the nozzle plate acceler-ation and deflection when the system is subjected tobase sawtooth shock excitation. This value of dampingis also an optimum damping for random base excita-tion if the isolation frequency is 30Hz. Therefore, anisolator with isolation frequency of 30Hz and dampingratio of 0.25 could be an optimum isolator for the jetimpingement cooling system considered here, subjectedto the harsh environment of shock and random basevibration. With such an isolator there will be an attenu-ation factor of about 15 at the nozzle plate, and chassisvibration travel of less than 2.5mm when subjected torandom base vibration, and normalized transmittedshock of 0.75 (i.e. equal to a transmitted shock of15 g in this case) and chassis vibration travel of3.6mm when subjected to shock input.

Acknowledgments

The authors would like to gratefully acknowledge the finan-cial and technical support of their funding bodies.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11.5

2

2.5

3

3.5

4

4.5

5

5.5

6x 10

−7

ωc=10Hz

ωc=20Hz

ωc=30Hz

ωc=40Hz


max

imum

def

lect

ion

(m)

Figure 17. Maximum deflection of the nozzle plate versus isolation damping ratio at different isolation natural frequencies.




Funding

This work was supported by the Defense Science

Organization of Singapore and Temasek Laboratories atNTU (grant number TL/DSOCL/0083/02).

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Design and analysis of shock and random The Author(s) 2013 ...ashkanhh.mit.edu/sites/default/files/images/JVC1.pdf · ATR chassis including two jet impingement chambers is modeled