FORCE-LIMITED VIBRATION TESTING APPROACH APPLIED TO RANDOM VIBRATION TEST OF SOLAR PAYLOAD

L. Trittoni (1), M.Martini (2)

(1),(2) ALENIA Spazio – Strada antica di Collegno ,253 , 10146 Turin, Italy E-mail: Laura.Trittoni@aleniaspazio.it, Massimo.Martini@aleniaspazio.it

Tel: + 39 011 7180349 – Fax: + 39 011 7180274

ABSTRACT

The flexibility of the Columbus Experiment Payload Adapter (CEPA) significantly influences the Random Vibration Environment (RVE) at SOLAR interface (I/F). Since a random qualification test in hard-mounted condition was foreseen, the design load factors would be exceeded if the RVE analytically derived at SOLAR to CEPA I/F would be directly applied. Therefore, an expressly developed, validated methodology has been adopted: based on the equivalence of resultant I/F forces in hard-mounted and soft-mounted condition (for corresponding main modes), notched random spectra have been derived and applied as test input. During the test activity, significant frequency reduction of the main resonances has been detected, imputable to I/F’s non-linearity, while the assumed amplification factor was confirmed. Therefore, the analytically defined input spectra have been adapted to the real dynamic behaviour. After a successful FEM model correlation activity, the effective masses computation has confirmed the correctness of main resonances identification and the achievement of the foreseen qualification loads.

INTRODUCTION

The European ISS modulus Columbus provides four mounting locations for external payloads, whose interface adapter is the CEPA plate. Therefore, in the frame of SOLAR project, the flexibility of the CEPA plate has an important influence to determine the dynamic environment applicable to SOLAR Payload. Since a random vibration test on EQM hard-mounted model (SOLAR + instruments dummies) was planned, it was not possible to directly apply to SOLAR the random input spectra specified to CEPA, because this input is subjected to such a modification/amplification due to CEPA dynamics. On the other hand, with the direct application of the Acceleration Spectral Density (ASD) analytically

derived at SOLAR to CEPA I/F points, the Random Vibration Load Factors (RVLF) defined for the whole SOLAR project and for each instrument would be exceeded. The problem has been overcome by performing an analysis activity finalised to define opportunely notched ASD input spectra which realise a condition of equivalence, in terms of RVLF, between hard mounted and soft mounted configuration.

1. RVLF DERIVATION BY STANDARD METHODS

RVLF are typically calculated using Miles’ Equation, which is based upon statistical analyses of induced acceleration spectra with a 3-sigma distribution. Miles’ Equation determines a load factor by assuming that the fundamental mode in each orthogonal direction will provide the primary response:

2/1

nn ASDfQ2

3RVLF ��

���

� ×××π×= (1)

where Q = Amplification factor, fn = System fundamental frequency (Hz),

ASDn= Acceleration Spectral Density at fn (g2/Hz)

For most components, a Q of 10 for all three directions should be used if not test data are available. Component frequencies are determined either by Normal Mode Analysis or sinusoidal sweep test.

For complex components in which a single dominant mode in each direction cannot be identified, the modal mass participation method may be used to provide a more realistic, less conservative load factor.

As a first step, a Normal Mode Analysis of the Finite Element Model (FEM) of the component with the boundary constrained in the flight configuration is performed and the mass participation of the model in each mode for each orthogonal direction is extracted.

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European Conference on Spacecraft Structures, Materials & Mechanical Testing 2005Noordwijk, The Netherlands, 10 – 12 May 2005 (ESA SP-581, August 2005)

1

The sum of the participating mass in all of the significant modes in each direction should add up to at least 80 percent of the total mass of the component.

Essentially, this method allows the use of multiple modes in the calculation of the RVLF by multiplying the contribution of each significant mode (RVLFi) by a ratio of the effective mass participating in the mode to the total component mass.

Each mass-weighted RVLFi is then root-sum-squared with the others to obtain the composite RVLF for that orthogonal direction.

2/1

Ni,N,iN,i

Ni, ASDQf2�

M

Meff3RVLF �

�

���

� ×××××= (2)

2/1

i

2N,iN RVLFRVLF ���

�

���

�= � (3)

where N = direction (X, Y, Z), i = mode number

The intrinsic limitation of this method resides in the fact that it does not allow taking into account the flexibility of the supporting structure. Therefore, it is not applicable to soft mounted structures.

2. RVLF DERIVATION BY RANDOM VIBRATION ANALYSIS

Miles’ formula can be also written as:

gMRVLF

2/1

i

2N,i

F

N ×

��

�

�

��

�

�

=�

(4)

where: 2/1

Ni,N,iN,iNi, ASDQf2�

gMeff3F ��

���

� ××××××= (5)

and where N = direction (X, Y, Z), i = mode number

Fi.N is the resultant of the interface forces.

Random Vibration Analysis, already used to derive the RVE in terms of ASD provides, instead, the single interfaces forces, in term of Force Spectral Density (FSD) and Force root mean square (Frms). The resultant of the interface forces cannot be directly computed from the single interface forces: in fact, by simply performing a sum of the single FSD, the resultant is overestimated, since the phase differences between the single interface forces are not taken into account.

Nevertheless, since the Random Vibration Analysis is only a post processing of the Frequency Response

Analysis, the resultant interface forces can be conveniently computed in this first step, where the phase information is available, and then squared (as the other transfer functions) to derive the resultant force spectral densities and the associated rms values.

Therefore, the following procedure has been set-up.

1. A frequency response analysis is performed, with unitary input

2. The interface forces at the constrained nodes are required, for each frequency, as real and imaginary part

3. The interface forces resultant is derived, for each frequency, as the Root Sum Square (RSS) of the SUM of the real parts and the SUM of the imaginary parts, that is:

( ) ( ) 2/12

Nk,

2

Nk,Nk, imagFrealFresF ����

�� += �� (6)

where k = frequency step number, N = direction (X, Y, Z)

4. The resultant FSD can be computed as:

N,k2

Nk,N,k SresFFSDres ×= (7)

where Sk,N = power spectral density of the input load

Two simple test cases have been developed to verify the method:

1. Rectangular homogeneous panel clamped at the 4 edges (symmetric case) 2. Rectangular homogeneous panel clamped at 3 edges (asymmetric case)

Both have been loaded with an homogeneous pressure field.

The obtained results are compared hereinafter for the two cases.

SYMMETRIC

MODE FREQ. (Hz) M11 M22 M331 79.07 0 0 84.122 166.20 0 0 03 208.45 0 0 04 270.59 0 0 7.55 393.76 0 0 06 427.96 0 0 07 485.01 0 0 3.97

% OF TOTAL 0 0 95.59

Table2-1: Modal basis

2

XY

Z

Output Set: Mode 1, 79.06585 HzDeformed(1.348): Total Translation

Fig. 2-1: Mode 1

Interface forces

1E-04

1E-03

1E-02

1E-01

1E+00

50 100 150 200 250 300 350 400 450 500

FREQ [Hz]

FOR

CES

[N]

Z res

Z1

Fig. 2-2: Frequency response - single I/F compared with resultant

Interface force resultant [N]

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

50 100 150 200 250 300 350 400 450 500

SUM RES INPUT LOAD

Fig. 2-3: Frequency response - resultant, sum and input load

Interface forces resultant

1E-04

1E-03

1E-02

1E-01

1E+00

50 100 150 200 250 300 350 400 450 500

Frequency [Hz]

FS

D [N

^2/H

z]

Z

Fig. 2-4: Random response –resultant

MODE f [Hz] PSD[Pa^2/Hz]

PSD[g^2/Hz]

g rms m eff X geffx

1 79.1 91.2 0.0 0.9 0.8 0.82 166.2 145.4 0.0 1.7 0.0 0.03 208.5 182.6 0.0 2.1 0.0 0.04 270.6 182.6 0.0 2.4 0.1 0.25 393.8 28.9 0.0 1.1 0.0 0.06 428.0 28.9 0.0 1.2 0.0 0.07 485.0 28.9 0.0 1.3 0.0 0.1

RLF Z2.4

Frms [N] M [kg] RLF [g]

8.423 1.102 2.3

Table 2-2: RLF computation (resultant and Miles)

ASYMMETRIC

MODE FREQ. (Hz) M11 M22 M331 43.74 0 0 64.472 103.34 0 0 22.583 175.74 0 0 0.224 246.52 0 0 5.665 306.58 0 0 0.676 414.96 0 0 07 439.75 0 0 1.44

% OF TOTAL 0 0 95.05

Table 2-3: Modal basis

XY

Z

Output Set: Mode 1, 43.7398 HzDefo rmed(2.448): To tal T ranslation

Fig. 2-5: Mode 1

Interface forces

1E-04

1E-03

1E-02

1E-01

1E+00

10 60 110 160 210 260 310 360 410 460

FREQ [Hz]

FO

RC

ES

[N]

Zres

Z1

Z31

Z621

Fig. 2-6: Frequency response - single I/F compared with resultant

Interface force [N]

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+ 00

10 60 110 160 210 260 310 360 410 460

SUM RES INPUT LOAD

Fig. 2-7: Frequency response - resultant, sum and input load

Interface force resultant

1E-04

1E-03

1E-02

1E-01

1E+00

10 60 110 160 210 260 310 360 410 460

Frequency [H z ]

FSD

[N^2

/Hz]

Z

Fig. 2-8: Random response – resultant

3

MODE f [Hz] PSD[Pa^2/Hz]

PSD[g^2/Hz]

g rms m eff X geffx

1 43.7 115.1 0.0 0.8 0.6 0.52 103.3 145.4 0.0 1.3 0.2 0.33 175.7 145.4 0.0 1.7 0.0 0.04 246.5 182.6 0.0 2.3 0.1 0.15 306.6 182.6 0.0 2.6 0.0 0.06 415.0 182.6 0.0 3.0 0.0 0.07 439.8 182.6 0.0 3.1 0.0 0.0

RLF Z1.8

Frms [N] M [kg] RLF [g]

6.084 1.102 1.7

Table 2-4: RLF computation (resultant and Miles)

From the comparison of the obtained results, it can be noticed that, while in the symmetric case there is no difference between resultant and sum of interface forces, in the asymmetric case the sum overestimates the response. This behaviour can be explained looking at the modal reaction forces: while in the symmetric case the reaction forces are always concordant (significant effective mass) or discordant (null effective mass), in the asymmetric case hybrid conditions occur. The complete agreement with Miles’ formula confirms the reliability of the method. In fact, in these simple cases, the structure is hard-mounted and therefore the same boundary conditions assumed by Miles’ formula are realised. In case of soft-mounted conditions, instead, the actual interface acceleration can be automatically considered for RLF estimation, avoiding the conservatism relating to the adoption of an envelope ASD. In addition, if a direct acoustic load is applied, its effect can be directly combined with the contribution of interface ASD.

3. RANDOM VIBRATION ANALYSES PERFORMED ON CPD FE MODEL

As a first step, two Random Vibration Analyses have been performed: � on the flight integrated model, applying the

Random Vibration Spectrum specified at CEPA I/F, with the purpose to define: 1. the Random Vibration Environment at SOLAR

I/F points comprehensive of CEPA dynamic 2. the I/F forces at CEPA to SOLAR I/F and the

related Random Vibration Load Factors (at SOLAR c.o.g.)

� on the flight hard-mounted model, applying the Random Vibration Spectrum defined as per point 1, with the purpose to define:

� the I/F forces at CEPA to SOLAR, Instruments and Ball bearings I/F’s and the related Random Vibration Load Factors (at SOLAR and instrument c.o.g.’s)

Then, the comparison of the I/F forces computed at CEPA to SOLAR I/F’s at steps 2 and 3 constitutes the basis for the derivation of new opportunely notched

random input spectra (in X, Y, and Z directions). The aim is to not exceed the Random Vibration Load Factors defined for the whole SOLAR project and for each instrument. A third Random Vibration Analysis has been performed on EQM hard-mounted model (SOLAR + Instruments dummies) and the already defined notched input spectra have been refined to take into account the Test Article behaviour.

The integrated FEM models of SOLAR CPD with CEPA (soft mounted condition) and without CEPA (hard mounted condition) have been used, as represented in Fig. 3.1.

Fig. 3-1: F.E.M. Model – CPD soft and hard mounted configuration

3.1 Qualification Input spectra and environment evaluation

PSD spectra given by ESA for CPD soft mounted configuration at CEPA frame active/passive bottom I/F are different spectra in X, Y, and Z directions (Fig. 3.1-1). The CPD input spectra are the maximum expected ones and are induced from the acoustic environment of 141 dB and so are used as Qualification levels.

PSD INPUT SPECTRA - CEPA I/F

0.001

0.01

0.1

10 100 1000 10000

Frequency [Hz]

PS

D [g

2 /Hz]

Input Y

Input X

Input Z

Fig. 3.1-1: Input PSD Spectra

In Fig.3.1-3 the RVE derived at CEPA to CPD I/F are reported, obtained by the averaged environment from the 72 I/F points between the CPD base-plate and

4

CEPA. The spectrum levels derived are obtained injecting the ESA defined flight input levels at the CEPA I/F points and following the acceleration combination schema (as per Fig. 3.1-2).

zo.o.p.

x(HX) i.p.

y(HY) i.p.

z(HZ) o.o.p.

Input [g2/Hz] Output [g2/Hz]

i.p.(x) due to o.o.p.

i.p.(y) due to o.o.p.

o.o.p. due to o.o.p.

i.p.y

y(HY) i.p.

z(HZ) o.o.p.

x(HX) i.p. i.p.(x) due to i.p.

z(HZ) o.o.p.

xx(HX) i.p.

y(HY) i.p.

o.o.p. due to i.p.

i.p.(y) due to i.p.

i.p.

+

+

+

i.p.(x)

i.p.(y)

o.o.p.(z)

+

+

+

Fig. 3.1-2: Acceleration combination schema

SPECTRUM LEVELS - CEPA TO CPD I/Fs - In Plane (Xcpd axis)

0.0001

0.001

0.01

0.1

1

10 100 1000

Freq. [Hz]

AS

D [g

2 /Hz]

Acc.Input at CEPA I/F ( Xcpd axis) : 3.1 grms

CMA strength verification : 6.78 grms

CMA+CEPA: 3.9 grms

SPECTRUM LEVELS - CEPA TO CPD I/Fs - In Plane (Ycpd axis)

0.0001

0.001

0.01

0.1

1

10 100 1000

Freq. [Hz]

AS

D [g

2 /Hz]

Acc. Input at CEPA I/F (Ycpd axis): 3.1 grms

CMA strength verification : 6.78 grms

CPD+CEPA: 3.63 grms

SPECTRUM LEVELS - CPD TO CEPA - OOP(Z)

0.0001

0.001

0.01

0.1

1

10 100 1000Freq. [Hz]

AS

D [g

2 /Hz]

Acc. Input at Zcpd axis: 3.2 grms

CMA strength verification : 6.78 grms

CMA+CEPA : 4.23 grms

Fig. 3.1-3: RVE at CEPA to CPD I/F – XCPD ,YCPD, ZCPD direction

As can be seen from Fig. 3.1-2, the RVE evaluated at CEPA to CPD interface is much higher in all the three axis directions, resulting also in higher grms values, with respect to the input level applied to CEPA (0.025 g2/Hz). As a consequence, the input random spectra specified at CEPA I/F cannot be directly applied to CPD without CEPA, since this input is subjected to such a modification/amplification due to CEPA dynamics that should induce a different I/F forcing function scenario.

3.2 I/F Forces comparison

In order to derive the I/F forces resultant and the RVLF (as per equation (6)), a frequency response analysis has been performed applying the acceleration of 1g for the entire range of frequencies. In this case, the FSD and grms are evaluated, for each of the three principal CPD directions (XCPD, YCPD and ZCPD), as the squared of the I/F Transfer Function (Apparent Mass in terms of [N/g]) of SOLAR CPD both hard and soft mounted. These transfer functions (in terms of Squared Apparent Mass Function), multiplied by ESA defined input acceleration spectra (Fig. 3.1-1) and by derived RVE in terms of [g2/Hz] for CPD hard mounted (Fig. 3.1-3), give respectively the equivalent FSD for CPD soft and hard mounted configuration. The relation used is as follow:

�

�� =�

��

∗�

��

Hz

NCPD_FSDHzgSpectra_Input_Acce

gNCPD_Mass_Apparent_Squared

22

22

(8)

For CPD hard mounted a comparison with the derived Miles RVLF shows a very good agreement with the grms obtained using the I/F force method:

METHOD X [grms] Y [grms] Z [grms]MILES EQ. 5.99 3.17 11.5I/F FORCES 5.87 3.1 11.44

RVLF

Table3.2-1: Comparison RVLF with Miles and I/F Forces

3.3 Method for RVE derivation

The definition of the new input RVE for the CPD without CEPA is based on the comparison of the I/F forces between the two configurations studied (Fig.3.3-1). The application of the derived environment at CEPA to CPD I/F (Fig.3.1-3) for CPD hard mounted lead to a too conservative environment in terms of FSD, resulting also in high value of RVLF (Fig.3.3-1 shows the FSD comparison for X, Y and Z direction).

5

X FSD AT CEPA TO CPD I/F's - COMPARISON CPD HARD MOUNTED vs INTEGRATED CPD WITH CEPA

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

10 100 1000Freq. [Hz]

FSD

[N2 /H

z]

FSD CPD SOFT MOUNTED RVLF:2.68 grms

FSD CPD hard mounted RVLF:6.06 grms

Y FSD AT CEPA TO CPD I/F's - COMPARISON CPD HARD MOUNTED vs INTEGRATED CPD WITH CEPA

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

10 100 1000Freq. [Hz]

FSD

[N2 /H

z]

FSDY CPD SOFT MOUNTED - RVLF: 2.08 g

FSDY CPD HARD MOUNTED [N^2/Hz] - RVLF: 3.49g

Z FSD AT CEPA TO CPD I/F's - COMPARISON CPD HARD MOUNTED vs INTEGRATED CPD WITH CEPA

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

10 100 1000Freq. [Hz]

[N2 /H

z]

FSDZ CPD HARD MOUNTED [N^2/Hz] - RVLF:10.98 g

FSDZ CPD SOFT MOUNTED [N^2/Hz] - RVLF: 5.56g

300

Fig. 3.3-1: FSD soft and hard mounted comparison

A preliminary approach based on the equivalence of the I/F forces at each frequency band between the two configuration using relation (8) is corrected from an analytically point of view but could lead to a high conservative level in the definition of the new spectra. In facts, as appears in Fig. 3.3-1, at 300 Hz in X direction it is necessary to inject an high level of acceleration to the hard mounted model in order to make an equivalence of force with the soft mounted one, which is at least one order of magnitude lower than the maximum value achieved by the soft mounted model at lower frequency. Starting from the previous results and in order to reduce the conservatism, a new approach has been defined based on the equivalence of the I/F forcing function for corresponding main modes in the two configurations. A Modal Assurance Criterion (MAC) has been used in order to evaluate the equivalence of the modal behaviour of the two models. Through the MAC criteria a list of correspondence modes for the 3 principal direction has been identified. The coupled mode shapes have been split in the three

principal axes X, Y and Z using the results of the effective masses relevant to CPD with CEPA and CPD with-out CEPA configurations (Fig.3.3-2).

MODE CYCLES T1 MODE CYCLES T1NO. FREQ. FRACTION NO. FREQ. FRACTION VALUE

2 26.5 28.68% 1 35.2 22.0% 0.61 23.0 0.47% 2 38.8 7.0% 0.616 61.8 5.06% 4 62.9 1.3% 0.597 63.9 1.97% 5 66.8 2.9% 0.549 66.6 5.36% 6 70.9 0.9% 0.57

14 80.1 0.09% 9 80.1 33.9% 0.8318 93.6 0.002% 13 93.7 0.1% 123 114.3 0.01% 18 114.4 0.01% 144 203.6 0.0001% 37 184.6 2.2% 0.61

CEPA+CPD CPD HARD MOUNTEDX DIRECTION

MAC

MODE CYCLES T2 MODE CYCLES T2NO. FREQ. FRACTION NO. FREQ. FRACTION VALUE

2 26.5 0.4% 1 35.1681 17.6% 0.61 23.0 42.1% 2 38.78 49.0% 0.617 63.9 6.4% 5 66.79 1.5% 0.548 65.0 0.3% 6 69.84 5.2% 0.59

12 75.8 0.4% 7 77.20 1.0% 0.8510 69.4 4.8% 12 90.26 3.9% 0.5231 133.6 0.01% 20 133.24 1.3% 0.88

MAC

Y DIRECTIONCEPA+CPD CPD HARD MOUNTED

MODE CYCLES T3 MODE CYCLES T3NO. FREQ. FRACTION NO. FREQ. FRACTION VALUE

2 26.5 5.6% 1 35.17 0.5% 0.61 23.0 0.9% 2 38.78 1.6% 0.613 45.49 0.8% 3 45.61 0.2% 16 61.8 9.3% 4 62.87 0.5% 0.597 63.9 0.5% 5 66.79 0.4% 0.549 66.6 13.0% 6 69.84 0.2% 0.57

14 80.1 0.01% 9 80.42 1.2% 0.8310 69.4 7.9% 12 90.26 9.8% 0.5221 101.73 0.01% 16 101.83 0.1% 1

MAC

Z DIRECTIONCEPA+CPD CPD HARD MOUNTED

Fig. 3.3-2: CPD modal coupling using MAC - XCPD YCPD and ZCPD direction

4. INPUT RANDOM SPECTRA DEFINITION FOR CPD QUALIFICATION TEST

Starting from the comparison between CPD I/F FSD in soft and hard mounted condition (with and without CEPA frame), manual notching profiles have been adopted in order to avoid structural over-testing of CPD test article (Figures 4-1, 4-2).

Fig. 4-1: CPD Test Article

6

Fig. 4-2: CPD Test Article mounted on shaker - excitation along the vertical Z-axis

4.1 Manual Notching profiles characterisation by Interface Forcing function comparisons

Fig. 4.1-1 shows the comparison between the I/F force resultant for X directions. The evidenced over testing has been limited through the application of a notched profile as per Fig. 4.1-2. The same approach has been utilised for the Y in plane and the Z out of plane CPD axes (Fig.4.1-3, 4.1-4). The predicted qualification environments for the Y and the Z direction of CPD are reported in Fig. 4.1-5 and 4.1-6. An important aspect is that the input qualification environment is not only subjected to notching approach but, also, needs to be increased (see. Fig 2-13 below 50 Hz) where the FSD in soft mounted condition is higher than in the hard mounted one. In the Z direction the input was augmented between 40 and 70 Hz with respect to the preliminary input derived through the first strength verification campaign of CPD.

FSD AT CEPA TO CPD I/F's - In Plane X direction

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

10 100 1000Freq. [Hz]

FSD

[N

2 /Hz]

FSD CPD NOTCHED 3sigmaRVLF: 5.4gFSD CPD HARD MOUNTED MODEL XdX 3sigmaRVLF: 8.27g

FSD CPD+CEPA SOFT MOUNTED XdX 3sigmaRVLF: 2.79g

OVERTESTINGNOTCHED

Fig. 4.1-1: Comparison between EQM Model of CPD hard mounted vs. CPD soft mounted I/F forces – X Direction

DEFINED TEST QUAL. SPECTRUM LEVEL - Xcpd axis

0.001

0.01

0.1

10 100 1000Freq. [Hz]

AS

D [g

2 /Hz]

X NOTCHED grms=6.61

X FLIGHT INPUT : 6.78 grms

Fig. 4.1-2: Predicted manual notching profile for in plane CPD X direction

FSD AT CEPA TO CPD I/F's - In Plane Y Direction

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

10 100 1000Freq. [Hz]

FS

D [N

2 /Hz]

FSD CPD NOTCHED YdY 3sigmaRVLF: 4.08g

CPD+CEPA SOFT MOUNTED FSDY 3sigmaRVLF: 2.18gCPD HARD MOUNTED FLIGHT MODEL YdY 3sigmaRVLF: 4.01g

Fig. 4.1-3: Comparison between EQM Model of CPD hard mounted vs. CPD soft mounted I/F forces – Y Direction

FSD AT CEPA TO CPD I/F's - Out of Plane Z

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

10 100 1000Freq. [Hz]

FSD

[N2 /H

z]

FSD CPD ZdZ NOTCHED 3sigmaRVLF: 9.93gCPD+CEPA SOFT MOUNTED FSD ZdZ 3sigmaRVLF: 5.7gFSDZ CPD HARD MOUNTED [N^2/Hz] - RVLF:10.98 g

NOTCHED

Fig. 4.1-4: Comparison between EQM Model of CPD hard mounted vs. CPD soft mounted I/F forces – Z direction

7

18

TRI-AXIAL ACC.

XCPD

ZCPD

TRI-AXIAL ACC. PILOT

TRI-AXIAL ACC. CO-PILOT

19

21

23

20

22

24

XCPD YCPD

ZCPD

DEFINED TEST QUAL. SPECTRUM LEVEL - Ycpd axis

0.001

0.01

0.1

10 100 1000 10000Freq. [Hz]

AS

D [

g2 /Hz]

Y NOTCHED INPUT : 6.75 grms

CMA strength verification : 6.78 grms

Fig. 4.1-5: Predicted manual notching profile for in plane CPD Y direction

DEFINED TEST QUAL. SPECTRUM LEVEL - Zcpd axis

0.001

0.01

0.1

10 100 1000 10000Freq. [Hz]

AS

D [g

2 /Hz]

Z NOTCHED INPUT : 6.76 grms

CMA strength verification : 6.78 grms

Fig. 4.1-6: Predicted manual notching profile for out of plane CPD Z direction

4.2 Automatic Notching profiles characterisation by Interface Forcing function comparisons – Indirect method

The qualification strategy adopted foresees an integrated test / analysis approach, where analytical data coming from the FEM simulations are combined with test laboratory measurements. For this reason, to prevent CPD structure from being damaged, it was useful to set up an automatic notching procedure of the input random environment. Therefore, the test instrumentation plan foresaw three-axial response accelerometers located on instruments I/F’s, ball bearings I/F’s, main structural parts and geometric c.o.g. The RVE at the corresponding FEM locations has been computed and on this basis the potential automatic notching monitor channels have been selected.

The accelerometers locations are sketched in Fig. 4.2-1.

2 1 3

4

5

6

10

9

12

11

13

15

TRI-AXIAL ACC.

XCPD YCPD

ZCPD

7

8

16

14

Fig. 4.2-1: Test set-up

It was important to check (in real time) that, around main resonance modes, the CPD did not exceed the predicted acceleration levels. Monitoring the acceleration levels, it is expected that also the predicted I/F forces levels over the main critical locations (i.e. Ball Bearings, instruments I/F’s) are controlled: indirect method.

5. TEST APPROACH

The test approach followed for the qualification of CPD is reported in Fig.5-1. The need to adopt this test approach derives by the fact that: � CPD FEM was not correlated before this test � The notching philosophy is based on I/F forces

computed at CPD/CEPA (soft mounted condition) while the I/F between CPD and shaker (hard mounted condition) is monitored in terms of accelerations (indirect method).

In order to properly qualify CPD, the reliability of the computed I/F forces has to be confirmed/tuned by the mode shapes correspondence between the hard mounted and soft mounted condition.

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Fig. 5-1: CPD Test approach

6. SINE LOW LEVEL (SLL) TEST, RESONANCE SEARCH AND Q FACTOR EVALUATION

According to the test approach defined in paragraph 5, the sine low level test (SLL) has been performed for each of the reference CPD axis (X, Y and Z), in order to retrieve the main resonance frequencies and the Q factors of the CMA EQM. A significant frequency shift has been detected for the main resonant frequencies over each axis; Table 5-1 reports the comparison between the main mode frequencies of CPD Test Article and test prediction FEM model:

Table 6-1: Modal Frequencies shifts between test article and FE prediction model (before updating)

The correspondence reported in Table 5-1 is based on a comparison between the accelerometers responses recorded during the sine tests over the main modes (imaginary part of the accelerations) and the analytical mode shapes computed by FE analysis.

The predicted Q factor (Q=10) has been confirmed since the amplitude of the peaks predicted and measured is the same. Furthermore, significant accelerometers have been identified on the basis of their response at the main resonant frequencies detected.

Test data results gave evidence, also, that reasonably all accelerometers, and especially the accelerometer A18 near the C.O.G of the CMA EQM, are representative of the main resonance frequencies for the X, Y and Z direction. In Fig.6-1 an example of frequency response comparison between predicted and measured acceleration levels at CPD c.o.g. is reported.

Fig. 6-1: Frequency response comparison between predicted and measured acceleration levels at CPD c.o.g. (X direction)

7. INPUT SPECTRUM MODIFICATION

On the basis of the SLL results, in order to qualify SOLAR CPD, due to the presence of main modes frequency shifts (see Table 6-1), the predicted input qualification environments have been modified. Since the Q factor (Q= 10) has been confirmed from the preliminary SLL, no modification of the predicted input ASD levels has been necessary, while modifications of the predicted manual notching have been introduced. Each accelerometer response has been considered in order to evaluate in order to: � Confirm or not of the linearity of the model � Confirm the adequacy of the assumed Q factor � Validate/modify the automatic notching predicted

levels For the X and Z direction, it was necessary to introduce a shift of the notching (Fig. 7.1 and 7.2).

DEFINED TEST QUALIFICATION SPECTRUM LEVEL - Xcpd

0.001

0.01

0.1

10 100 1000 10000Fre q. [Hz]

AS

D [g

2 /Hz]

X PREDICTED QUAL. INPUT : 6.61 grms

X TEST QUAL INPUT grms=6.66

SHIFT

Fig. 7-1: X CPD direction – Qual. Test input spectrum

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D E F INE D T E S T Q UAL . S PE C T RUM L E V E L - Zcp d

0 .0 01

0 .01

0 .1

1 0 1 0 0 10 0 0 1 0 0 00F re q . [H z ]

AS

D [g

2 /Hz]

Z TE S T Q UA L. INP UT: 6.78 grm s

Z P RE D IC TE D Q UA L . INP UT : 6 .7 6 g rm s

SHIF T

Fig. 7-2: Z CPD direction – Qual. Test input spectrum

For the Y direction the input in the frequency range of 20-40 Hz has been doubled due to a poor dynamic in that range of frequency.

T EST QUALIFICATION SPECT RUM LEVEL Ycpd

1.0E-03

1.0E-02

1.0E-01

10 100 1000 10000Freq. [Hz]

AS

D [g

^2/H

z]

Y PREDICTED QUAL. INPUT : 6.75 grms

Y TEST QUAL. INPUT : 6.77 grms

SHIFT

Fig. 7-3: Y CPD direction – Qual. Test input spectrum

7.1 Automatic notching definition / confirmation The results obtained at random low levels (–9dB, –6dB and –3dB) constituted the basis for the definition / confirmation of the predicted automatic notching. What has been evidenced was: � The necessity to add automatic notching channels at

ball bearing locations due to the presence of high levels of ASD, especially in the frequency range between 700-2000 Hz, with high grms values ���� non linearity behaviour. In this range of frequency the notched levels were defined on the basis of the margin between the I/F Forces in hard and soft mounted condition (at least 1 order of magnitude).

� The confirmation of the radial main support bending mode at 90 Hz (A10 location – confirmation of the automatic notching predicted, registration of a spike ASD at 90 Hz) already present in the FE prediction model.

� The presence of high levels of ASD at 120 Hz at sun sensor I/F (A13 location – registration of a spike ASD at 120 Hz).

� The Q factor evaluated over the main resonance as Q = √(PSDout / PSDin) ≈ 7.5 ÷ 9.7 confirms the goodness of the analytical one (Q = 10) and, as a consequence, the predicted notching levels.

BALL BEARING LOCATIONS - A09 - INPUT IN-PLANE XCPD AXIS

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

10 100 1000 10000Freq. [Hz]

[g^2

/Hz]

HIGH ASD LEVELS

Fig. 7.1-1: Example of tested Ball Bearing non linearity

0dB - ASD NOTCHED INPUT X vs. REFERENCE

1.0E-03

1.0E-02

1.0E-01

10 100 1000 10000

Freq. [Hz]

[g^2

/Hz]

REFERENCE INPUT

AUTOMATIC NOTCHEDINPUT

Fig. 7.1-2: Example of automatic notching channel versus qualification Input due to ball bearings non linearities

� Confirmation of the accelerometer A18 as the most

representative of CPD C.O.G. In fact, all the main resonance frequencies of the test article were recorded at this location. Hence, it has been always included in the automatic notching channels.

8. CPD RANDOM VIBRATION QUALIFICATION CONFIRMATION

Due to the above considerations and to the correspondence of the main test modes with the predicted ones (considering the shift of the main peaks, see Table 5-1), it was possible to confirm the qualification of CPD on the basis of the following parameters: � grms values recorded by channel A18 (representative

of the C.o.G of the test article) compared with the predicted ones based on I/F force limiting

C.o.G MEASURED C.o.G PREDICTED

Direction grms value grms value X 8.13 4.9 Y 5.15 3.4 Z 5.2 5.8

Table 8-1: Comparison of measured and predicted qualification grms at C.o.G.

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� grms of test inputs spectra compared with the predicted ones based on I/F force limiting

TESTED INPUT PREDICTED INPUT

Direction grms value grms value X 6.66 6.61 Y 6.77 6.75 Z 6.78 6.76

Table 8-2: Comparison of measured and predicted qualification grms at C.o.G.

� Measured ASD values at each main frequency compared with the predicted ones based on I/F force limiting

� Comparison between the sine low levels runs before and after the random qualification test – structural integrity � no major shift has been detected

� Visual inspection – structural integrity � no damage was showed

9. CPD FEM MODEL UPDATING On the basis of the results of the SLL and RVE test performed on CPD Test Article, the FEM model has been updated in order to better correlate the results of the test campaign. This correlation activity was based mainly on mass distribution and stiffness properties upgrading. A ‘silhouette’ of the test CPD EQM HW has been built considering the accelerometers position:

Fig. 9-1 CPD Silhouette

Figures below show the modes shapes comparison between TAM (Test Analytical Model) and FEM after updating.

Fig. 9-2 Main mode 3: 40.1 Hz - Translation along Y axis

Fig. 9-3 Main mode 4: 45.5 Hz - Translation along X axis

Fig. 9-4 Main mode 5: 58.8 Hz - Translation along Z axis

Table 9-1 reports the comparison between the main modes frequencies of CPD-EQM Test Article and updated FEM model:

CPD-EQM Test Article hard mounted

CPD-EQM FEM Model hard mounted (before updating)

X [Hz] Y [Hz] Z [Hz] X [Hz] Y [Hz] Z [Hz] ∆∆∆∆f [%] 17.7 17.7 7.1% 28 29.2 4.4%

34 36.9 8.4% 38 40.1 5.5%

43 45.5 5.8% 60 58.8 -5.6%

Table 9-1 Modal Frequencies shifts between test article and FE Model after updating

Table 9-2 reports the effective masses of the CPD-EQM FEM model after updating:

FEM EQM hard mounted (after updating) MODE

N. FREQUENCY

[Hz] T1 [%]

T2 [%]

T3 [%]

R1 [%]

R2 [%]

R3 [%]

1 17.7 1% 0% 2% 0% 13% 0% 2 29.2 1% 63% 0% 60% 1% 18% 3 36.9 24% 0% 0% 1% 17% 1% 4 40.1 12% 14% 0% 6% 10% 2% 5 44.8 0% 0% 1% 0% 0% 0% 6 45.5 32% 1% 0% 0% 24% 45% 7 58.8 0% 0% 55% 6% 13% 0%

Table 9-2 SOLAR-CPD EQM FE Modal effective masses [%] – Hard mounted with-out CEPA

FEM MODEL AFTER UPDATING [Hz] 17.7 29.2 36.9 40.1 44.8 45.5 58.8 TEST MODES 1 2 3 4 5 6 7 17.7 1 12% 1% 4% 3% 1% 2% 0% 28 2 1% 59% 0% 1% 1% 0% 0% 38 3 1% 8% 9% 10% 0% 11% 3% 43 4 5% 1% 11% 6% 20% 67% 0% 60 5 0% 1% 1% 0% 46% 0% 52%

Table 9-3 MAC performed between test article and FE Model after updating (*)

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(*) Note: this MAC table does not derive from a modal test made on the CPD EQM hardware, but only from a comparison of the accelerometers responses recorded during a sine test over the main modes (imaginary part of the accelerations); however this type of computation has been useful in order to better understand the behaviour of the test article and to have another decisional parameter for the correlation with the analytical mode shapes. For these reasons and also due to the poor instrumentation plan, the MAC values are not so high.

10. CONCLUSIONS New test input spectra based on I/F force method have been defined with both the targets to not exceed the design loads of the relevant items (CMA, Instruments and Ball Bearings) and to subject CMA in hard mounted configuration (test) to a still conservative environment with respect to the soft mounted one (flight) in terms of interface force levels. This target has been achieved, confirming the goodness of the results obtained from the CMA qualification point of view. In fact, the purpose of the test is not to reach the design loads of the project, but to demonstrate that, when injected with an equivalent flight random qualification environment, in terms of equivalent FSD, the structure is able to withstand the achieved loads. A manual notching profile has been defined, to properly control the expected outputs versus design loads. In addition, during test execution, the automatic notching procedure has been activated to prevent unexpected structural response amplifications. The here presented results, confirmed the random vibration qualification of CPD. Moreover, the successive random analyses performed with the updated and correlated F.E. model gave a sound contribution for the definition and confirmation of the RV qualification environment applicable to the SOLAR mounted instruments and units (SOVIM, SOLACES, SOLSPEC, CU and Sun sensor).

11. ACRONYMS

CoG Center of Gravity CPD Coarse Pointing Device CMA CPD Mechanical Assembly SOLAR CPD Coarse Pointing Device-Solar version CEPA Columbus External Payload Adapter FEM Finite Element Method

NSTS National Space Transport System FSD Force Spectral Density ASD Acceleration Spectral Density RVLF Random Vibration Load Factor RVE Random Vibration Environment AMS Apparent Mass Squared CPD = CMA + CU + SYSTEM ITEMS (sun sensor, thermal h/w, harness) SLL = Sine Low Level RLL= Random Low level

12. REFERENCES

[R1] T.D. Scharton, “Force Limited Vibration Testing Monograph”, NASA RP-1403, May 1997

[R2]L. Trittoni, M. Martini, “Force-limited acceleration spectra derivation by Random Vibration Analysis: methodological cases and industrial application”, 6th DCSSS conference, July 2004

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