Mechanical sizing of ule parts

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Mechanical sizing of ule parts

S. Allée, V. Lebat, E. Perrot, S. Orsingher

To cite this version:

S. Allée, V. Lebat, E. Perrot, S. Orsingher. Mechanical sizing of ule parts. 13th European Conf. on Spacecraft Structures, Materials & Environmental Testing, Apr 2014, BRAUNSCHWEIG, Germany.

�hal-01079656�

Mechanical sizing of ule parts.

S. Allée *, V. Lebat, E. Perrot, S. Orsingher *

13th European Conf. on Spacecraft Structures, Materials & Environmental Testing

BRAUNSCHWEIG, ALLEMAGNE 1-4 avril 2014

TP 2014-509

Mechanical sizing of ule parts.

Dimensionnement mécanique des pièces en ULE.

par

S. Allée *, V. Lebat, E. Perrot, S. Orsingher *

* MECANO ID, Toulouse

Résumé traduit :

La mission GRACE FO est conduite par le JPL (Jet Propulsion Laboratory). Cette mission, en orbite autour de la Terre, produira un nouveau modèle précis du champ de gravité terrestre, notamment des données pour le climat, pendant au moins les cinq prochaines années.

L'ONERA développe et fabrique deux accéléromètres électrostatiques, et a sous-traité à MECANO ID les calculs mécaniques. Les accéléromètres spatiaux développés par l'ONERA sont principalement composés d'une masse d'épreuve suspendue électro-statiquement dans une cage d'électrode (cœur de l'instrument). Dans le cas de l'accéléromètre GRACE FO, la cage d'électrode est composée de 3 plaques en ULE (Ultra Low Expansion Glass : une vitro-céramique). Des butées mécaniques métalliques sont utilisées pour limiter la course libre de la masse d'épreuve à l'intérieur de la cage (±12µm dans l'axe X et ±25µm dans les axes Y/Z).

Pendant les vibrations dues au lanceur, la masse d'épreuve heurte les butées mécaniques. A cause de la fragilité des plaques en ULE, l'évaluation de force de l'impact de la masse sur ces butées est d'une grande importance.

Pour les vibrations aléatoires, nous utilisons un moyen d'essai en vibration (pot vibrant) pour obtenir une excitation temporelle. Comme cette excitation est plus ou moins homogène au cours du temps, un faible intervalle de temps contenant l'accélération maximale est sélectionnée et comparée à l'accélération à 3 sigma du spectre d'accélération théorique pour vérifier que l’intervalle choisit est conservatif.

Pour le choc, un spectre SRS a été spécifié. Pour dimensionner les pièces en ULE dans le domaine transitoire, plusieurs excitations extraient d'une base de données d'essais ont été sélectionnées afin d'être également conservatif.

Ces entrées transitoires ont été utilisées dans un modèle élément fini spécifique du cœur. Ce modèle a été construit sur le logiciel Dytran, spécialisé dans les simulations de très courte durée. Les forces d''impact sur les butées ont été calculées puis appliquées sur le modèle global linéaire de l'instrument utilisant le logiciel Nastran.

Pour finir, une méthodologie spécifique a été définie et utilisée pour dimensionner les pièces en ULE. Cette approche est basée sur une étude statistique qui analyse séparément les zones de traction et celles de compression.

Dans ce papier, nous décrivons en détails les hypothèses, le modèle élément fini, la sélection des intervalles de temps représentatifs de l'excitation dynamique et le dimensionnement mécaniques des plaques en ULE (incluant le calcul des marges de sécurité).

Cette activité traite principalement des thèmes suivants : - Architecture mécanique, design et ingénierie

- Dynamique des structures, incluant le choc et les micro-vibrations.

NB : Ce Tiré à part fait référence au Document d'Accompagnement de Publication DMPH14013

MECHANICAL SIZING OF ULE PARTS

S. Allée

^a

, V. Lebat

^b

, E. Perrot

^b

, S.Orsingher

^a

a

MECANO ID

9 rue Paul Charrier - 31100 TOULOUSE – FRANCE mecano@mecano-id.fr

b

ONERA – The French Aerospace Lab

29 avenue de la division Leclerc, BP72 – F-92322 CHÂTILLON cedex – FRANCE vincent.lebat@onera.fr

eddy.perrot@onera.fr

ABSTRACT

The objective of the activity done by MECANO ID for the GRACE FO program was to perform the mechanical sizing of the electrostatic accelerometer developed and manufactured by ONERA (The French Aerospace Lab) and in particular the plates of its core, made of ULE glass (Ultra Low Expansion glass: a titanium silicate glass).

This document describes the methodology employed and the results obtained to achieve this purpose.

1. INTRODUCTION

The GRACE FO mission is led by the JPL (Jet

Propulsion Laboratory) and GFZ

(GeoForschungsZentrum). This mission is an Earth- orbiting mission that will produce new accurate models of the Earth’ gravity field and its variations, providing global climatic data during five year at least.

ONERA is developing and manufacturing 2 identical electrostatic accelerometers, and has sub-contracted to MECANO ID the mechanical sizing of the accelerometer.

The space accelerometers developed by ONERA are based on the principle of a proof mass electro-statically suspended in an electrode cage (core). The accelerations the proof mass is submitted to during the mission in orbit are compensated by electrostatic forces applied by electrodes of a servo-loop to the proof mass.

The GRACE FO accelerometer Sensor Unit (SU) is mainly composed of (Fig. 1):

 The Sensor Unit Mechanics (SUM), with:

o A sole plate, fixed on the spacecraft, o An accelerometer core,

o A tight housing and a passive vacuum apparatus, to maintain very low pressure level inside the housing,

 The Front End Electronic Unit (FEEU) with 4 PCBs.

Figure 1. Main parts of GRACE FO accelerometer The accelerometer core is mainly composed of a proof mass located into a cage of electrodes plates. For GRACE FO accelerometer, the proof mass is in titanium, while the electrodes are made of ULE glass.

Metallic mechanical stops are used to limit the low free motion of the proof mass within the electrode cage (±12µm in X axis and ±25µm in Y/Z axes), and to avoid short circuits between the proof mass and the electrodes. These stops are implemented within the ULE plates (Fig. 2).

Figure 2. Views of the core of the accelerometer SUM

FEEU

Pumping system Sock assembly

Housing

Accelerometer core Sole plate

Stops (angular and

vertical)

ULE plates

Proof mass Sole plate

_______________________________________

Proc. ‘13th European Conf. on Spacecraft Structures, Materials & Environmental Testing’,

Braunschweig, Germany, 1–4 April 2014 (ESA SP-727, June 2014)

2. ENVIRONMENTAL LOADS

The launch submits the equipment to high vibration levels, so are the proto-qualification tests of the accelerometer.

As the proof mass is free, it hits the stops during the vibration duration. Due to the fragile nature of ULE, the evaluation of the forces at proof mass / stops impact is of the almost importance.

ULE being subject to static fatigue, evaluation of the stresses due to preload of the screws is also mandatory.

During the course of the pre-development of the accelerometer, some mechanical analyses are necessary to assess the design of the most critical issues:

- Resistance of ULE and metallic parts against vibrations and shocks of the proof mass, against flatness defects of the sole plate (3µm), against preload of the screws and against temperature excursions.

- Stability of bolted joints mainly against temperature evolutions, between the sole plate and the accelerometer core (the stability is imposed by some performances reasons of the accelerometer).

2.1. Evaluation of impact forces of the proof mass on the stops

For random vibrations, we used our vibrations means (numerically controlled electro-dynamic shakers) to obtain a time excitation. As the excitation is somewhat homogeneous over the time, a short time excitation containing the maximum acceleration value is selected and tuned to be conservative compared to the 3  acceleration theoretically induced by a random spectrum.

These transient inputs have been used on a specific Finite Element Model of the core (ULE parts). As the proof mass free motion is non-linear, non-linear dynamics software has to be used. In our case, we used MSC.Dytran, nonlinear quick dynamics solver (step by step direct integration).

Impact forces at stops were computed to be applied in a linear global FEM of the accelerometer using MSC.Nastran software.

3. MECHANICAL SIZING OF ULE PARTS

3.1. Presentation of ULE parts

The ULE plates of the core (two carrier plates and one ring plate) are of various surface finishes: polished surfaces and ultrasonic machine (Onera process) finished surfaces (Fig. 3).

Carrier plates:

Ring plate:

Figure 3. ULE plates

3.2. Presentation of the FEM

The mechanical sizing of the ULE parts is done with a Finite Element Model representative of the accelerometer built for MSC.Nastran software (Fig. 4), composed of a total of 670 000 nodes and 240 000 elements (of 1

^st

and 2

^nd

order):

FEM of the accelerometer: Detail of the SUM:

Detail of the core:

Figure 4. FEM of the accelerometer and details

3.3. Methodology

A specific methodology has been used to size ULE parts. It is based on a statistic approach which analyzes separately the traction and compression areas. This methodology has been developed by Onera and approved on GOCE accelerometers.

ULE is a breakable material with a significant

difference between tensile strength and compressive

strength. Thus, to evaluate the margin of safety, the

Von Mises stress in not appropriated; the damaging

stress 

^*_ULE

and the principal stress 

_1max-ULE

should be

used.

3.3.1. Damaging stress

The damaging stress is calculated with the formula (Eq. 1):

v eq

ULE  R

 ^  (1)

With:

 

_eq

: maximum Von Mises stress

 R _{v ( 1}  _{) 3 ( 1 2}  ₎   _H  _eq 

3

2   



 

_H

₌ 

_kk

/3: hydrostatic stress

The margin of safety is then calculated with the formula (Eq. 2):

_

^*

*

ULE ULE FOS ULE

MOS 



   (2)

With:

 FOS: factor of safety,

 

_ULE

: design stress (allowable stress), depending on the surface finish,

  _ULE ^* : damaging stress.

3.3.2. Principal stress

According to [1], the design stress 

_ULE

is derived from the characteristic strength 

_0-ULE

divided by a factor of safety f

FOS-ULE

(Eq. 3):

ULE FOS ULE f ULE _

  ⁰ 

 (3)

The factor of safety f

FOS-ULE

is factorized as (Eq. 4):

F P A ULE

FOS f f f

f _  (4)

The formulae for the individual factors of safety are derived on the basis of the Weibull distribution. This distribution function is widely used in product lifetime statistics.

The area factor f

A

is calculated according to the following formula (Eq. 5); this formula assumes constant stress within the loaded area:

/  1

 

 



 

L A S V

f S ⁽⁵⁾

With:

 S

V

: area of the tensile stress loaded surface,

 S

L

: reference surface area,

  : Weibull factor.

The formula for the probability factor f

P

is (Eq. 6):

/  1

1 ln 1

1

 

 









V P

F

f (6)

With:

 F

V

: allowable probability of failure.

In the case for a stress load constant in time, the formula for the calculation of the fatigue factor f

F

is (Eq. 7):

  ⁿ

P A F t V f f R n f

/ 1 0

1 



 



 

  ⁽⁷⁾

Where:

 t

V

: stress load duration time for the application,

 R: stress increase rate for measuring 

₀

_,

 n: environmental stress corrosion coefficient.

Coefficients S

L

, R, n, (1-F

V

) depend on the type of material, see [2]; while coefficients  _and 

₀

_also depend on the surface finish.

The area S

V

of the tensile stress loaded surface is calculated from the finite element model results, for all load cases.

Three margins of safety were studied:

 For the area where the tensile stress is positive,

 For the area where the tensile stress is larger than 20MPa

 For the area where the tensile stress is larger than 80% of the maximum principal stress.

The margin of safety is then calculated with the formula (Eq. 8):

ULE ULE FOS ULE

MOS

 



max max 1

_ 



 (8)

With:

 FOS: factor of safety,

 

_ULE

: design stress (allowable stress), depending on the surface finish,

 

_1max-ULE

: principal stress (direct input from MSC.Nastran calculation).

3.4. Results

Thus, the analyses on the accelerometer led to determine margins of safety in the ULE parts of the core.

The approach with the damaging stress eventually

turned out to be more conservative than the approach

with the principal stress.

The results can be illustrated through margin of safety distributions (Fig. 5).

Random PFM X-axis Thermo-elastic case TE_min

Figure 5. Margins of safety in ULE parts On top of these results, the distortions of the ULE plates under maximum preload of the core screws were calculated at different locations as indicated hereinafter (Fig. 6 and Fig. 7).

Figure 6. Location of node lines for distortion calculation

Figure 7. ULE plate distortion

We can see that the plates have a concave shaped distortion.

3.5. Fracture control analysis

A fracture control analysis was performed on the ULE parts of the core of the accelerometer.

It consists in the sustained stress analysis. This analysis permits to define the maximal size of an initial crack which can be accepted, and to assert whether the visual inspection with binoculars is sufficient to detect these defaults.

The success criterion for the analysis is recalled hereinafter (Tab. 1):

Analysis Criterion

Safe life No crack growth propagation after 4 life cycles Table 1. Safe life criterion

3.5.1. Methodology

The following methodology is used. It is based on the NASGRO software NASGLS, which is a module of ESACRACK.

The growth equation involved in this calculation is, as specified, a Paris-type equation (Eq. 8):

AK n

dt

da  (8)

From [1], we deduced (Eq. 9):

C n

K

A   _{0 1} ^ (9)

where K

1C

and 

₀

are material coefficients.

The detectable flaw depth is defined as a third of the calculated initial flaw depth (Eq. 10):

3

0 / a

a _d  (10 )

For each ULE part, the potential risk areas are identified, corresponding to areas defined by the minimum safety margins previously calculated. For these areas, the maximum stresses computed for each load case are extracted, and then input in NASGLS through the sequence of load events.

Note that the standard scatter factor of 4 has been included by running the stress spectrum 4 times.

3.5.2. Results

For each ULE part, several NASGLS analyses were done for to simulate all crack cases and all loadings.

An example of results is presented in Fig. 9:

Figure 9. Example of the fracture control analysis From these analyses, the minimum initial calculated flaw depth allowing to sustain 4 life cycles proved to be compatible with the inspection mean (binoculars), as requested.

Node line 1

Node line 2

Node line 3

4. CONCLUSION

In that paper, we presented a computation approach implemented to evaluate the stress levels in the ULE parts used for the GRACE FO accelerometer, whose design is in consolidation.

Acknowledgements

This analysis has been performed in the frame of the JPL subcontract to ONERA

MECANO ID is indebted to ONERA for having permitted the realisation of these analyses and for having allowed publication of this paper.

References

1. Optics for Devices, SCHOTT North America, Inc (2004) Design strength of optical glass and ZERODUR TIE-33

2. Gulati, S.T. (1994). Relative Impact of Manufacturing vs. Service Flaws on Design of Glass Articles. In Design for Manufacturing of Ceramic Components, Amer.

Ceram. Soc.