(L.L.F.) CURVES & PSD DERIVATION METHOD FOREQUIPMENT MOUNTED ON SATELLITE PANELS

Andrea Ceresetti (*), Thijs Van Der Laan (#)

(*) ALENIA SPAZIO - Torino, Italy; (#) ESA/ESTEC - Noordwijk, The Netherlands

ABSTRACTThis paper presents, for all those cases of equipment mounted on structural panels of a satellite, theapproach of derivation of the Limit Load Factor (L.L.F.) curves related to the equipment mechanicaldesign as well as the Acceleration Power Spectral Density (PSD) input spectra related to theequipment qualification vibration tests.

KeywordsLimit load, effective/theoretical amplification factor, (L.L.F.) curve, random vibration spectra,notching, hardmounted test, power spectral density, vibroacoustic.

NomenclatureA area of an impinged structural element (m2) Ppeak sound induced pressure peak (N/m2)BW frequency bandwidth (Hz) PSD acceleration power spectral density (g2/Hz)c viscous damping of an oscillator (N s/m) PSDg ground acceleration PSD (g2/Hz)k stiffness of an oscillator (N/m) SPL Q quality factor [1/(2ξ)]fn, Fn natural frequency of an oscillator (Hz) SPL 1/3-1 oct. band pressure noise (dB) relative to P0fi,ff,fc band frequencies (initial, final, center) (Hz) ü acceleration (g) or (m/s2)f1 ‘Source’ uncoupled natural frequency [w1/(2π)] üg base excitation acceleration (g) or (m/s2)f2 ‘Load’ uncoupled natural frequency [w2/(2π)] WP pressure power spectral density (N/m2) 2/(Hz)g gravity acceleration factor g= 9.81 (m/s2) w1 ’Source ’ uncoupled circular frequency √[k1/m1]H acceleration transfer function H=H(w) w2 ‘Load’ uncoupled circular frequency √[k2/m2]m mass of an oscillator (kg) ξ1 ‘Source’ critical damping ratio [c1 /(2√(k1 m1))]M mass of an acoustically impinged structure (kg) ξ2 ‘Load’ critical damping ratio [c2 /(2√(k2 m2))]oop,ip out of plane, in plane directions µ ’Load’ to ’Source’ mass ratio [m2/m1]P0 reference pressure noise P0=2*E-5 (N/m2) φ ’Load to ’Source’ frequency ratio [f2/f1]=[w2/w1]Pr.m.s sound induced pressure r.m.s. (N/m2) Γn modal mass % (for n th mode)

1. INTRODUCTIONDedicated (L.L.F.) curves can be produced for equipment structural dimensioning purpose, tailoredto each equipment-panel of a satellite. Usually, a set of three curves is generated, one for eachprincipal direction of the panel, by considering the time consistent superposition of the mainmechanical environmental contributions to the ‘limit load’, namely: quasi static, low frequencytransients, random vibration and acoustic noise. As a general approach for high frequency loads, bothpressure and acceleration power spectral densities can be treated in a similar manner to derive theacceleration responses, by using an equivalent random-acoustic PSD response spectra method,applicable to those panels classified as ‘relevant acoustic receivers’. Once defined the randomvibration spectra at equipment mounting interface, and considering the dynamic couplingcharacteristics, then typical (L.L.F.) curves are derived whose sloped behaviour is a function of theequipment mass. Moreover, considering that so far, based on the most important requirementssources, the equipment PSD spectra definition method is simply based on “rules of inverseproportionality” vs. the equipment mass, this paper also puts in evidence which is the expectedinfluence of each dynamic parameter, like: geometrical characteristics, mass and surface density offull/empty panel and equipment, minimum required stiffness, equipment mounting position on panel,acoustic profile characteristics. The approach of generating equipment PSD spectra and (L.L.F.)curves, has recently been implemented in the space industry for both the HERSCHEL & PLANCKService Modules (SVM) during the design development phase, in progress nowadays. In practice, theapproach explained here might become a general-purpose method for reducing both design/test

acceleration overloads. In fact, traditional methods sometimes can easily introduce some artificialcriticalities and consequent risk of overdesign/overtesting as far as the equipment structural aspects.

2. DESCRIPTIONIn current satellite technology, equipment are normally grouped and mounted on dedicated platformsvery often constituted by honeycombs (e.g. aluminium core with aluminium or carbon face sheets).Each panel assembly (platform + all mounted equipment) can be defined as an ‘equipment-panel’.For example Fig. 1 shows a satellite weighting about 3.5 tons. comprising a 1.0 ton. SVM, that isconstituted by eight equipment-panels, as shown in Fig. 2 exploded view.

Fig. 1 3.5 tons. Satellite (Overall View) Fig. 2 1.0 ton. SVM Structure (Exploded View)

Above equipment-panel layout is also termed as ‘satellite box-type’, being the equipment mountedagainst the sidewalls (attached each other in a box shape) and resulting in direct contact with thevibroacoustic environment of the Spacecraft (S/C) fairing. Thus, both the panels and their mountedequipment are exposed, especially during the first phases of the flight, to low and high frequencyenvironments that will induce, at a certain instant of the mission, the limit acceleration load. Bydefinition, the ‘limit load’ represents the maximum load expected to be acting on a structure duringits design service life. In general, for satellite equipment-panels, the acceleration limit load is reachedduring the lift-off (L/O) phase, from the following main acceleration loads:

- Quasi Static (QS) + Low Transient (LT) Loads: (QSL)- Acoustic Loads: (AC)- Random Vibration Loads: (RV)

3. ACCELERATION LOADS MATRIXUsually, a typical 3 x 6 loads combination matrix is considered for S/C structures, see Tab. i.

Load Sets Linear Accelerations (g) Angular Accelerations (rad/sec2)

1 ±LLFx ±QSLy ±QSLz ± QSLRx ± QSLRy ± QSLRz

2 ±QSLx ±LLFy ±QSLz ± QSLRx ± QSLRy ± QSLRz

3 ±QSLx ±QSLy ±LLFz ± QSLRx ± QSLRy ± QSLRz

Tab. i Acceleration Loads Matrix

In particular, three (3) load sets result from the accelerations combination, where for each load set,the LLF is generated by considering simultaneous QSL loads with all possible sign (±) combinations,whilst the RV and AC (due to the low probability of peaks occurrence) are considered acting just oneaxis by a time. For simplicity a local co-ordinate system (r,t,l) is more suitable for panels geometry:

� r = normal to the panel surface (out-of-plane)� t = parallel to the panel short side (in-plane 1)� l = parallel to the panel long side (in-plane 2)

SVM

So, for each load set/local direction j=(r,t,l) a number of eight (8) load cases is established, where theLLF value is the term in the matrix main diagonal. Several methods are available in literature toderive the LLF from individual load contributions; however, the most commonly used method is toconsider the Square Root of the Sum of the Squares (SRSS) for QSL, AC, RV as defined in eq. [1].

(LLF) j = [(QSL)2j +( AC)2

j + (RV)2j]

1/2 [1]

Once the acceleration limit loads being evaluated, a Design Factor (DF) can be applied to get thedesign loads. Depending on project requirements, typical DF can be in the range of [1.0…to...2.0].

3.1 Acceleration Loads Matrix for Equipment-panelsThe equipment-panels acceleration matrix is of the same type of Tab. i. However, in this particularcase, rotational accelerations can be disregarded due to the limited dimensions of the structures. Theindividual loads qualitatively can be considered as : (QSL) low-medium; (AC) medium-high; (RV) ~

3.2 Acceleration Loads Matrix for EquipmentSimilarly to above, the same kind of loads already described can be identified. The individual loadcontributions qualitatively can be considered as: (QSL) medium; (AC) ~; (RV) medium-high.However for an equipment case, proper acceleration amplifications due to dynamic coupling with theequipment-panel must be considered. In particular, due to the equipment typical high stiffness, theamplifications are particularly relevant for RV, whilst are very limited for QSL. In practice, theequipment load matrix can be conceived to contain in the main diagonal the effects of the RVamplification. So, for each equipment-panel, an equipment load matrix can be defined as per Tab. ii,where the LLF is represented by a ‘curve’ correlating the equipment limit acceleration (g) versus itsmass (kg). Details about the (L.L.F.) curve philosophy are provided in {Ref.1}, {Ref.2}, {Ref.3}.

Out-of-plane In-plane (1-2)Load Sets( r ) ( t ) (l )

1 ± (L.L.F.)Curve(r) ± QSL(t) ± QSL(l)

2 ± QSL(r) ± (L.L.F.)Curve(t) ± QSL(l)

3 ± QSL(r) ± QSL(t) ± (L.L.F.)Curve(l)

Tab. ii Equipment Acceleration Loads Matrix

For equipment, the RV acceleration is mainly due to random vibrations acting at the equipment-panelinterface (I/F), that was originally produced by acoustic loads. Usually, a strong difference can benoticed between ’hard mounted condition’ and ‘flight configuration’. The reason is related to theeffects of the so-called Effective Amplification Factor (Qeff) that is always lower than equipmentQuality Factor (Q). The Qeff can be defined as the Input/Output (I/O) accelerations ratio, see eq. [2].

(Qeff) = (ü output /ü input) < (Q) [2]

For a Two-Degree of Freedom System (TDFS) ‘Source + Load’, subjected to a random vibration, theQeff formulations are given in {Ref.2}. However, the Qeff worst case is always obtained in tunedconditions (φ=1), being Qeff reaching the maximum expected value (Qeff*). The expression of Qeff* fora TDFS case is given by eq. [3], whose related dynamic parameters are defined in eq. [4] and eq. [5].In particular, in eq. [4] the ⟨ ü 2 ⟩ represent the mean square accelerations for the TDFS masses‘Source’m1 and ‘Load’ m2 (being the random vibrations of probabilistic nature).

Qeff*={[(ξξξξ1 (1+µµµµ) +ξξξξ2(1+3µµµµ+µµµµ2 )+4[ξξξξ13 + ξξξξ1

2ξξξξ2 (2+µµµµ)+ξξξξ1 ξξξξ22 (2+µµµµ)+ξξξξ2

3 (1+µµµµ)]+16 ξξξξ12 ξξξξ2

2 (ξξξξ1 +ξξξξ2 )] /

[µµµµ ξξξξ1+ξξξξ2 (µµµµ2+µµµµ)+4[ξξξξ1

3 µµµµ + ξξξξ12ξξξξ2 (1+µµµµ) +ξξξξ1ξξξξ2

2 (2+µµµµ) +ξξξξ23(1+µµµµ)]+16 ξξξξ1

2ξξξξ2 [(ξξξξ1

2 + ξξξξ22) + 2 ξξξξ1 ξξξξ2]]}

1/2 [3]

Qeff = √√√√(< ü22> / < ü1

2>) [4]

Qeff* = Qeff (φφφφ=1) [5]

It is evidenced here that the phenomenon of the effective amplification factor (applied for example todefine notching in vibration testing, see {Ref.4}) does not exclusively occur for random or acousticvibrations, but is a very general phenomenon, valid for all vibration types (e.g. dynamic absorbertheory is related to sine loads). The trend of eq. [3] shows that Qeff* is an inverse function of (µ). Allabove facts represent the analytical basis for equipment (L.L.F.) curve derivation approach.

4. VIBROACOUSTIC LOADSAs previously discussed, the equipment-panels AC represents the only significant high frequencyload contribution to the equipment (L.L.F.) curve. So the AC is the main source of equipment RV.Therefore, acoustically induced random vibrations on panels have been investigated and compared,as far as the following aspects are concerned:

4.1) Equipment-panels theoretical acoustic loads4.2) Equipment parametric PSD requirements4.3) Equipment-panels vibroacoustic test data4.4) PSD criteria comparison

4.1 Equipment-panels Theoretical Acoustic LoadsWhen a structure is subjected to an acoustic field, the Peak Pressure (Ppeak) can be assessed by eq. [7],where the Sound Power Spectral Density (WP) is treated similarly to the case of an AccelerationPower Spectral Density (PSD) in random vibration. The “acoustic” Miles equation is applied, see eq.[6], where the WP is calculated by eq. [12].

Pr.m.s. = [(ππππ/2) • Q• Fn • WP]1/2 [6]

Ppeak = 3 • Pr.m.s. [7]

The formulas eq. [8] thru eq. [12] are also introduced.

Fn ≡≡≡≡ fc = (fi • ff)1/2 [8]

For a typical noise pressure level (SPL) in dB defined at 1/3 or at 1 octave band spectrum, theresulting bandwidth is defined by eq. [9]; so for a certain frequency (Fn= fc) the bandwidth will be:

For 1/3 oct. spectrum: BW=(ff-fi)= 0.231• fc = 0.231 • Fn [9-1]

For 1 oct. spectrum: BW=(ff-fi)= (1/2)1/2 • fc = 0.707 • Fn [9-2]From the general definition of Noise Spectral Pressure (SPL) in (dB), the WP results:

SPL= 20 • log(P1/P0) (dB) [10]

P1=P0 • 10(SPL/20) [11]

WP=(P12)/BW =(P02 • 10(SPL/10))/BW [12]

The application of eq. [6] is a nearly exact solution for a structure having a dynamic behaviour SingleDegree of Freedom System (SDOF) like. On the other hand, for all cases of structures having severalglobal modes of vibration, the modal responses must be weighted on the square of the modal masses(Γn)

2. However, for typical cases of noise impingement over relevant acoustic receivers (e.g.structures with low mass density M/A < 100 (kg/m2) as meteoroids shields, equipment-panels, etc..)the dynamic behaviour of these structures is typically quite near to a SDOF, so that Miles formulaassociated to the global mode is deemed adequate and in general conservative with respect to exactsolution. Once obtained for a certain condition the Ppeak (N/m2), the corresponding Acoustic PeakAcceleration (ACpeak) in (g) units is given by eq. [13].

AC peak= [A/(M • g)] • Ppeak [13]

For example, when considering a structure as an ideal SDOF acoustic receiver with (Q=10), theacoustic noise environment of the Space Shuttle Cargo Bay 1/3 Oct-141dB (OASPL) should inducesome WP and Ppeak response spectra as shown in Fig. 3.

Fig. 3 Spectral Pressures for Space Shuttle Cargo Bay Noise (1/3 oct-141dB OASPL) for Q=10

Thus, for a generic case of a structure of a certain (M2/A2) ratio, the ACpeak2 can be analyticallyderived by simply scaling the results available from a previously known case (M1/A1) and ACpeak1,being applicable from eq. [13] the following proportionality law:

(ACpeak1/ACpeak2)=(Ppeak1/Ppeak2) • (A1/M1)/(A2/M2) [14]

Moreover, in order to derive the global accelerations acting at a structure Centre of Gravity (c.o.g.),an equivalence between AC & RV accelerations can be introduced as per eq. [15].

ACpeak ≡≡≡≡ RVpeak [15]

In other words, it is assumed that the peak acceleration AC produced by a SDOF under acousticimpingement being equivalent to the peak acceleration RV produced on same SDOF by a BaseExcitation Random Vibration PSDg, see Fig. 4 schematics. Consequently, the equivalence betweenAC and RV, in (g) units, is established as follows:

ACpeak ≡≡≡≡ RVpeak = 3 • √√√√ ⟨⟨⟨⟨ü12⟩⟩⟩⟩ [16]

From Fig. 4, the Acceleration Transfer Function (Hü1) can be defined as the ratio between I/O accelerations. The main formulations from SDOF random vibration theory are reported in eq. [17] thru eq. [21], where the applicable integration field is between [-∞..........+∞].

Hü1 = ü1 / üg [17]

Hü1=[(2iwξξξξ1wn +wn2)/(-w2+2i wξξξξ1 wn+wn

2)] [18]

PSD1 = PSDg • Hü12 [19]

Q2 =( ∫∫∫∫PSD1dw / ∫∫∫∫PSDgdw)=⟨⟨⟨⟨ü12⟩⟩⟩⟩////⟨⟨⟨⟨üg

2⟩⟩⟩⟩ [20]

⟨⟨⟨⟨ü12⟩⟩⟩⟩=∫∫∫∫PSD1 dw=∫∫∫∫Hü1

2PSDg dw [21]

Moreover, in case of PSDg=constant, the PSDg can Fig. 4 SDOF- Base Excitation Modelbe taken out from the integrals, and the theoreticalsolution of eq. [21] in terms of SDOF mean squareresponse is given by eq. [22].

10 100 1 103

1 104

110112

114116

118120

122124126

128130

132134

136138

140SHUTTLE Spectrum 1/3 oct-141 dB(OASPL)

CENTER FREQUENCY [Hz)

NOISE PRESSURE LEVEL

SPLi

FCi

ity [Pa^2/Hz]

10 100 1 103

1 104

0.1

1

10

100

1 103

PRESSURE Power Spectral Density

CENTER FREQUENCY (Hz)

PRESSURE Power Dens

WPi

FCi

[Pa]

10 100 1 103

1 104

100

1 103

1 104

PEAK PRESSURE for [Q=10]

CENTER FREQUENCY (Hz)

PEAK PRESSURE

Ppeaki

FCi

PSDg PSD1

⟨⟨⟨⟨ü1 2⟩⟩⟩⟩ ==== [[[[ (PSDg • wn/4) •(1+(2 ξξξξ)2)/(2222 ξξξξ ) ] [22]

Above equation slightly differs from the so calledMiles formula by the factor (Ψ = 1+(2ξ)2); anywayfor most S/C structural materials ξ<<1, Ψ≈1. In thiscase eq. [22] reduces to the Miles formula eq. [23].

⟨⟨⟨⟨ü12⟩⟩⟩⟩====[[[[((((PSDg • wn/4)•Q]====[[[[(ππππ/2)•Q•Fn•PSDg] [23]

For a SDOF case, the major contribution to aboveintegrals is within the bell-shaped transfer functionzone; thereby some approximate formulations likeeq. [24] and eq. [25] can be introduced.

PSD1Peak ≈ PSDg • Q2 [24]

⟨⟨⟨⟨ü12⟩⟩⟩⟩ //// ⟨⟨⟨⟨üg

2⟩⟩⟩⟩ ≈ ( PSD1Peak / PSDg ) [25] Fig.5 Response Spectrum for Shuttle (M/A=50)

Finally, due to the PSDg equivalent excitation, the expected PSD1 plateau producing the ACpeak (g)can be obtained by eq. [26], where the PSD1 profile corresponds to the PSD1Peak spectrum maxima, seeFig. 5. So, eq. [26] can be used as baseline for the derivation of equipment I/F input PSD plateau.

PSD1 ≡≡≡≡ PSD1Peak = WP • (Q/g) 2 • (A/M) 2 (PSD plateau in g2/Hz) [26]

Considering again the example of the Space Shuttle Cargo Bay noise of Fig. 3, for a structure havingQ=10 and (M/A)=50 (Kg/m2); in this case the equivalence for RV-AC in terms of PSD1 “responsespectra” leads to the results shown in Fig. 5.

4.2 Equipment Parametric PSD RequirementsFrom the experience gained on designing and testing past S/C projects, the main launch Authoritieshave established some parametric criteria for the definition of equipment random vibrationqualification spectra. In particular from {Ref.5} and {Ref.6} the task of derivation of the equipmentqualification random vibration test input profiles is simply based on a ‘rule of inverseproportionality’ with respect to the equipment mass. These criteria are investigated in the following.♦ NASA-GSFC CriteriaAccording to{Ref.5}for a Shuttle P/L mounted equipment of mass (m) located “anywhere”, the qual.test spectrum is given by Tab. iii and eq. [27]; the slope (dB/oct.) is fixed for all mass figures.

For m > 22.7 Kg: PSD(m) = K • [22.7/m] [27-a]For m ≤ 22.7 Kg: PSD(m) = K (K = 0.15 for all directions) [27-b]

Frequency(Hz)

Level PSD(g2/Hz)

Slope(dB/oct.)

Qual. TestDuration

20-50 y1- PSD(m) +650-600 PSD(m) 0

600-2000 PSD(m) - y2 -4.52.5

min./ axis

Tab. iii NASA-GSFC - Equipment Qualification Test Criteria

♦ ESA-ECSS CriteriaAccording to{Ref.6}, for all equipment cases of mass (m) < 50 (kg) located on “external panels” or“unknown S/C location”, the qualification test spectrum is given by Tab. iv and eq. [28].

10 100 1 103

1 104

1 105

1 104

1 103

0.01

0.1

1Equivalent PSD I/O spectra[M/A=50;Q=10]

FREQUENCY (Hz)

POWER SPECTRAL DENSITY

PSDIi

PSDOi

FCi

10 100 1 103

1 104

0.1

1

10AC-peak (g) for [M/A=50][Q=10]

FREQUENCY (Hz)

PEAK ACCELERATION [g]

ACpeaki

FCi

PSD1

ACpeak

For m < 50 Kg: PSD(m) = Ko,i • [m+20]/[m+1] [28]

(Ko = 0.12 for out of plane direction (oop); Ki = 0.05 for in plane directions (ip))

Frequency (Hz)

Level PSD(g2/Hz)

Slope(dB/oct)

Qual. TestDuration

20-100 x1 - PSD(m) +3100-300 PSD(m) 0300-2000 PSD(m) - x2 -5

2.5min./ axis

Tab. iv ESA-ECSS - Equipment Qualification Test Criteria

♦ NASA-ESA Criteria ComparisonFor an equipment of parametric mass [0.1..…50] (kg), the above PSD criteria comparison is shown inTab. v. The expected peak acceleration response (g) from Miles formula is shown in Tab. vi.

PSD(m) (g2/Hz) vs.Mass (kg)!

0.1 0.5 1 2 5 10 20 50

ESA-PSS-oop 2.19 1.64 1.26 .88 .5 .33 .23 .16ESA-PSS–ip .91 .68 .53 .37 .21 .14 .10 .07NASA- x,y,z .15 .15 .15 .15 .15 .15 .15 .07

Tab. v NASA-ESA Criteria Comparison for Equipment Parametric PSD(m) Plateau

RVpeak (g) vs. Mass (kg) !Fn=100/200/300 Hz; Q=10

0.1 0.5 1 2 5 10 20 50

ESA-PSS-oop 176/249/ 305 152/215/ 264 133/189/ 231 111/158/ 193 84/119/146 68/97/118 57/ 81/ 99 48/67/82

ESA-PSS–ip 113/160/ 196 98/ 139/ 170 87/ 122/ 150 72/ 102/ 125 54/ 77/ 94 44/63/77 38/53/ 65 31/ 44/54

NASA- x,y,z 46 / 65 / 80 46 / 65 / 80 46 / 65 / 80 46 / 65 / 80 46 / 65 / 80 46/65/80 46/65/80 31/44/54

Tab. vi Expected RVpeak (g) from Parametric PSD Criteria for 100/200/300 (Hz) Equipment (Q=10)

4.3 Equipment-panels Vibroacoustic Test DataFrom the vibroacoustic tests campaigns of some recently developed ESA satellites, a set ofmeasurements relevant to the max. PSD ‘clipped plateau’ at equipment mounting I/F of SVM panelshas been gathered, see Fig. 6 thru Fig. 11. In particular the PSD data from three different spacecraftacoustic qualification tests: XMM, ROSETTA, INTEGRAL have been analysed, whose acousticprofiles are shown in Tab. vii. Besides, for comparison purpose Tab. vii also shows the acousticqualification test requirement for HERSCHEL satellite, which will be taken as a calculation example.

Fig. 6 INTEGRAL-(STM) Test 144 dB (OASPL) Fig. 7 XMM-(FM) Test scaled to 147 dB (OASPL) SVM PSD vs. Mass Density (kg/m2) SVM PSD vs. Mass Density (ESA-source)

0,001

0,01

0,1

1

10

1 10 100 1000

EQUIPMENT-PANEL Mass Density [Kg/m^2]

PSD

[g

^2/H

z]

(oop) axis (i-p) axes

0,001

0,01

0,1

1

10

1 10 100 1000

EQUIPMENT-PANEL Mass Density [Kg/m^2]

PS

D

[g^2

/Hz]

(oop) axis

Fig. 8 XMM-(STM)- Test at 147 dB (OASPL) Fig. 9 ROSETTA(FM)-Test scaled 144 dB (OASPL) SVM PSD vs. Mass Density (ESA-source) SVM PSD vs. Mass Density (ESA-source)

Fig. 10 INTEGRAL- Qual. Test 144 dB (OASPL) Fig. 11 XMM-Qual.Test 147 dB (OASPL) SVM PSD (oop) vs. Equipment mass (kg) SVM PSD (oop) vs. Equipment mass (kg)

1 Oct. Band Centre Frequency (Hz)

XMM SPL [dB]

ROSETTA SPL [dB]

INTEGRAL SPL [dB]

HERSCHELSPL [dB]

31.563

125250500100020004000

133.6134.9140.3143.6139.6134.6129.1120

134.8136.5139.9136.8131.6125.6

119 119

135136140137131125118

132134139143138132128124

OASPL [dB] 147 144 144 146

Tab. vii ESA Spacecrafts - Vibroacoustic Qualification Test Requirements (P0=2*10-5 (Pa))

4.4 PSD Criteria ComparisonA PSD comparison has been performed, considering some equivalent acoustic loading conditions. Inpractice, no scaling of data shown in Fig. 6 thru Fig. 11 has been applied, since qualification profilesof Tab. vii for XMM, INTEGRAL, ROSETTA have different OASPL but the expected theoreticalPSD1 (oop) from eq. [26] result to be rather similar in all cases, see Fig. 12 at least in the range[50…150] Hz (which is typical for equipment-panels). So, in order to define an equipment “limitanalytical” PSD requirement, the max. spectral PSD of Fig.12 can be considered (e.g for XMM and

0,001

0,01

0,1

1

10

1 10 100 1000

EQUIPMENT-PANEL Mass Density [Kg/m^2]

PS

D

[g^2

/Hz]

(oop) axis (i-p) axes

0,001

0,01

0,1

1

10

1 10 100 1000

EQUIPMENT-PANEL Mass Density [Kg/m^2]

PS

D

[g^2

/Hz]

(oop) axis

0,001

0,01

0,1

1

10

1 10 100 1000

EQUIPMENT Mass [Kg]

PS

D

[g^2

/Hz]

(oop) axis

0,001

0,01

0,1

1

10

1 10 100 1000

EQUIPMENT Mass [Kg]

PSD

[g

^2/H

z]

(oop) axis

HERSCHEL the PSD results at 250 Hz while for ROSETTA / INTEGRAL the results at 150 Hz).Finally, Fig. 13 and Fig. 14 respectively compare the theoretical, parametric and PSD test data.

Fig. 12 Comparison of Theoretical PSD plateau and ACpeak (oop) Response Spectra

Fig. 13 Equipment I/F PSD Analytical vs.Test Data Fig. 14 Equipment I/F PSD Parametric vs.Test Data PSD vs. Equipment-panel mass density(kg/m2) PSD vs. Equipment mass (kg)

From Fig. 13 and Fig. 14, the following considerations are drawn:

- The PSD (oop) levels very often appear to be one order of magnitude higher than the (ip) ones.- Comparing the PSD (oop) from various S/C SVM the correlation degree of PSD plateau vs. panel

mass density (Fig. 6 thru Fig. 9) is more significant than vs. equipment mass (Fig. 10, Fig. 11).- A trend of inverse proportionality exists between PSD (oop) and equipment-panel mass density.- An apparent trend of inverse proportionality exists between PSD (oop) and equipment mass.

When comparing the PSD measurements vs. the equipment mass, the co-variance of data results ~ 0.In other words, it can be said: “heavy equipment are always mounted on heavy equipment-panels”whilst, “heavy equipment cannot be mounted on light equipment-panels”. So, it is pointed out thatdue to the effect of equipment-panels acoustic receiver characteristics, the PSD (oop) plateauresponse seems to be driven by the equipment-panel mass density rather than by the equipment mass.

Summarising the results reported in the above graphs, it is underlined that:

1) From S/C test data, the PSD (oop) plateau is always found in the range [50.. 250] Hz, which is ingood correlation with theoretical expectations of Fig. 12 and eq. [26]. In practice, the first twobending modes of S/C equipment-panels, normally lie below 250 Hz, and drive the max. PSD.

0,001

0,01

0,1

1

10

1 10 100 1000

EQUIPMENT-PANEL Mass Density [Kg/m^2]

PS

D

[g^2

/Hz]

PSD (oop) eq. [ 26 ]

PSD (ip)eq.[26] • (Ki /Ko)

0,001

0,01

0,1

1

10

1 10 100 1000

EQUIPMENT Mass [Kg]

PS

D

[g^2

/Hz]

Parametric: ESAPSD (oop) eq. [28]

Parametric: NASAPSD (oop) eq. [27]

10 100 1 103

1 104

0.1

1

10PEAK Acceleration (g) for [M/A=50][Q=10]

FREQUENCY (Hz)

PEAK ACCELERATION [g]

Apeak1i

Apeak2i

Apeak3i

Apeak4 i

FCi

1. XMM2. ROSETTA3. INTEGRAL4. HERSCHEL-PLANK

1

21

31

41

10 100 1 103

1 104

1 104

1 103

0.01

0.1

1

Equivalent PSD Output [M/A=50] ; [Q=10]

FREQUENCY (Hz)

POWER SPECTRAL DENSITY [g^2

PSDeqO1i

PSDeqO2i

PSDeqO3i

PSDeqO4i

FCi

1. XMM2. ROSETTA3. INTEGRAL4. HERSCHEL-PLANK

1

42

3

2) The PSD plateau when considered as a function of the equipment-panel mass density (Fig. 13)seems to be in a better correlation than when considered function of equipment mass (Fig. 14).

3) The PSD (ip) response is low; usually a PSD factor ratio (Ko / Ki ) = 2.4 is deemed conservative.

4) For equipment-panels, due to typical geometry, the PSD max. is generally found at their (c.o.g.).

5) For any kind of acoustic spectrum applied, a theoretical ACpeak is expected at equipment-panel(c.o.g.) and can be analytically assessed as a function of SPL and structure dynamics. Moreover,the ACpeak value can be thought as ‘acceleration input’ at the equipment mounting I/F.

5. EQUIPMENT (L.L.F.) CURVE & PSD INPUT

5.1 General CriteriaFrom previous considerations, the eq. [7] and eq. [13] enable the derivation of ACpeak (g) at equipment-panel (c.o.g.) and eq. [26] defines the PSD (g2/Hz) plateau. So, conservatively associating the Qeff* ofeq. [3], the equipment response (g) can be derived; similarly to Qeff*, such a response will be a curve.

5.2 (L.L.F.) Curve - Application Case An example of derivation of (L.L.F.) curve has been considered for HERSCHEL-SVM panel (-y).

5.2.1. Input Data for (L.L.F.) Curves DerivationConsider the equipment-panel(-y) layout shown in Fig. 2. The physical properties budget is given inTab. viii . The eigenvalues FEM result of the fully loaded panel (see Fig. 15) is given in Tab. ix. Thequalification spectrum of Tab. vii has been considered. An assy frequency of 100 Hz has beenconservatively assumed for ACpeak, WP and the corresponding equipment PSD (oop) requirement hasbeen evaluated in such a case. From frequency transient run of HERSCHEL-SVM FEM (being theCLA not performed yet) it results: QSL ≤ 16 (g) all axes of equipment-panel(-y); QSL ≤ 25(g) allaxes for equipment. The RV is negligible for equipment-panel, while AC ≈ 6.6 (g) (oop axis). TheAC is negligible for equipment. Finally, for all structures a critical damping ξ=5% was assumed.

EquipmentNASTRAN as “RBE3”

FEMGrid

Equip.Mass(kg)

PanelArea(m2)

TotalMass(kg)

MassDensity(kg/m2)

FHLCU 1383 11FHHRI 1392 11

FHHRH-1 1480 5.3FHHRH-2 1480 5.3

FHLSU 90000 12Assy (cog) 3943 -

1.38 53.6 ~ 39

Tab. viii SVM Panel(-y) Physical Properties

Fully LoadedSVM Panel(-y)

Mass(kg)

Frequency (Hz)(oop) axis

ModalMass %

Y FEM=(oop)53.6 72.5

260.8381.6

8452

Tab. ix SVM Panel(-y) FEM Modal Results (oop) Fig. 15 HERSCHEL-SVM Panel(-y) FEM

90000

1480

3943(c.o.g.)

1392

1111111383

DummyEquipment at cog

5.2.2. Equipment (L.L.F.) curves & PSD The PSD results shown in Tab. x have been derived from eq. [26] on the basis of the ESA-ECSS

trapezium profile of Tab. iv. The corresponding equipment (L.L.F.) curves are depicted in Fig. 16.

Freq. (Hz) PSD (oop) (g2/Hz) PSD (ip) (g2/Hz) Slope (dB/oct) time20-50 0.124 – 0.31 0.052 – 0.13 +3

50-300 0.31 0.13 0300-2000 0.31–13.3E-3 0.13 – 5.6E-3 -5

13.62 (g-rms) 8.83 (g-rms)

2.5 min. / axis

Tab. x Equipment Qualification Test Spectra for the Equipment-panel(-y) of HERSCHEL-SVM

Fig. 16 Equipment (L.L.F.) Curves for the Equipment-panel(-y) of HERSCHEL-SVM

5.2.3 FEM AnalysisA FEM of the equipment-panel(-y) has been runtaking into account a PSD1 equivalent plateaucorresponding to the response at about 72.5 (Hz),in accordance to FEM modal result of Tab. ix andtheoretical expectations of eq. [26]. Moreover, inorder to assess equipment effective amplifications, aSDOF (m,c,k)‘dummy equipment’ was considered,mounted at panel(-y) (c.o.g.), with parametric massof [m=0.1, 1.0, 10] (kg) and a Fn=100 (Hz) (e.g.the worst case corresponding to the HERSCHEL Fig. 17 FEM–Equipment-panel(-y) PSD (oop)equipment minimum stiffness requirement).The PSD I/O results are shown in Fig. 17. The results oftwo extreme conditions of dummy equipment (µ=0.2 and µ=0.002 ) are shown in Fig. 18 and Fig. 19.

Fig. 18 FEM I/O PSD (oop)-10 (kg) Equipment Fig. 19 FEM I/O PSD (oop)-0.1 (kg) Equipment

EQUIPMENT MASS (m2) [Kg]

0.01 0.1 1 10 1000

10

20

30

40

50EQUIPMENT (L.L.F.) Curve (i-p) axes

EQUIPMENT MASS (m2) [Kg]

LIMIT LOAD FACTOR (L.L.

LLFi( )µ( )inc

m2( )µ

0.01 0.1 1 10 1000

20

40

60

80

100EQUIPMENT (L.L.F.) Curve (o-o-p) axis

EQUIPMENT MASS (m2) [Kg]

LIMIT LOAD FACTOR (L.L

LLFo( )µ( )inc

m2( )µ

L.F.) [g]

Equipment-Panel (-y) (m2/m1=_ = 0.2)-Dummy Eqp. 2.4 grms-PANEL (cog) 1.4 grms

Equipment-Panel (-y) (m2/m1=_ = 0.002) -Dummy Eqp. 6.8 grms -PANEL (cog) 1.4 grms

Equipment-Panel (-y)- FHLCU 1.6 grms- FHRRI 1.4 grms- FHHRH 1.2 grms- FHLSU 1.4 grms- PANEL(cog) 1.4 grms

5.2.4 Loads ComparisonFrom above, the FEM results are always encompassed by (L.L.F.) curve. So, eventhough the (LLF)curve formulation is conservative, especially for heavy equipment cases the related (L.L.F.) valuesare by far lower than those derived by using parametric approaches, see Tab. vi. A comparison of theresponse (g) for (oop) axis for a 100/200/300 (Hz) equipment with (Q=10) is shown in Tab. xi.

ACCELERATIONS (g)for Equipment (oop) axis

SVM Panel (-y)

Equip.Mass(kg)

(L.L.F.) Curve(QSL=25 g)

(see Fig. 16)

NASA Parametric CriteriaMiles formula to eq. [27]

Equipment: 100/200/300 Hz

ESA Parametric CriteriaMiles formula to eq. [28]

Equipment: 100/200/300 HzFHLCU 11 30 46 / 65 / 80 66 / 94 / 115FHHRI 11 30 46 / 65 / 80 66 / 94 / 115

FHHRH1-2 5.3 32 46 / 65 / 80 82 / 117 / 142FHLSU 12 29 46 / 65 / 80 65 / 91 / 112

Dummy Equipmentlocated at Panel

(c.o.g.)

101.00.1

304352

46 / 65 / 8046 / 65/ 8046 / 65 / 80

68 / 97 / 118133 / 189 / 231176 / 249 / 305

Tab. xi Panel(-y) - Equipment Response (g) Comparison for Fn=100/200/300 (Hz) (oop) (Q=10)

6. CONCLUSIONSFor equipment mounted on satellite panels, analytical methods based on the dynamic couplingimpedance can be used to derive more realistic (L.L.F.) design curves and PSD test criteria.

7. REFERENCES{1} M. Trubert -NASA-JPL-D5882 “Mass Acceleration Curve for S/C Structural Design“ (Nov. 89).{2} A. Ceresetti - ALENIA Spazio “Limit Load Factor Curve (L.L.F.) for Preliminary Mechanical Design of Components for Space Missions – An Attempt of Mathematical Justification” European Conference on Spacecraft Structures, Materials and Mechanical Test, Braunschweig (D) (Nov. 98) ESA-SP-428/pg.179-186.{3} A. Ceresetti - ALENIA Spazio “Limit Load Factor (L.L.F.) Curves for Spacecraft Elements” European Conference on S/C, Materials and Mechanical Testing, Noordwijk (NL)-(Nov. 2000) ESA-SP-468/pg.175-183.{4} NASA-HDBK-7004 “Force Limited Vibration Testing Handbook” - (May 2000).{5} NASA, GEVS-SE Rev. A “General Environmental Verification Specification for STS & ELV Payloads, Subsystems, Components” GSFC (June 1996).{6} ESA, ECSS-E-10-03-Draft 01H, European Cooperation for Space Standardization “Space Engineering Testing” (Oct. 1999).

GENERAL SUMMARY SESSION SUMMARY▲ ▲

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