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The Experiences of Esterline Advanced Sensors using SAMCEF® in the development of Aeronautic Sensors

Paul CARRICO , Designer /Materials Expert Esterline Advanced Sensors – AUXITROL SA – Bourges (France)

Abstract : This presentation comprises 3 main discussion topics :

o A quick overview of FEA’s performance over the past few years using the SAMCEF® module for sensors development (THERMAL®, MECANO®, DYNAM®, REPDYN®, SPECTRAL®)

o The ability of SAMCEF® to interface with external routines for increased reliability i.e. leading to a good correlation of the modelling to the test measurements : a specific development including an hyperelastic material is presented for model analysis (modal analysis and dynamic response)

o A few examples which highlight gains in efficiency (the ability to launch multiple runs, automatic post-processing …)

1- Quick insight to Esterline Advanced Sensors

Esterline Advanced Sensors offers ours customers a broad range of high precision

solutions for aeronautics (cockpit, airframe and engine) and derivative products for

marine, defence and the industrial sector. It is based on a strong company culture,

shown by our 936 employees, who are driven by high added-value customer service,

reliability and the best operational performance of our products. The company asserts its

leadership in the field of sensors for pressure, temperature, speed, torque and analogue

indicators.

The ability to master programs - from design to development and through industrial to

production - and to work with partners in different fields of application makes Esterline

Advanced Sensors a tier one supplier.

Each new product incorporates our world class pedigree, but is unique and application

specific in line with customer requirements. Examples of our sensors and harnesses are

shown in Fig 1.

Fig 1 : Engine and aircraft views featuring some Esterline Advanced Sensors products (The Engine depicted above is a Rolls Royce Trent and has been used for illustrative purposes only. Esterline Advanced Sensors is

only one of many suppliers to this power unit and therefore it is used here for the ease of understanding sensor applications and

part locations)




2- Introduction

Finite Elements Analyses (FEA) correlated with physical testing, is a key step in

certifying new Sensor designs. This work allows Esterline to determine many aspects

of a design, including the safety margin, a fundamental part of the design validation

process.

Furthermore FEA’s are crucial towards extrapolating the mechanical behaviour of our

sensors in extreme conditions where physical tests are unrealistic, such as very low

temperatures (typically in cryogenic conditions), very high temperatures and high

frequency environments.

In our Temperature Design Office in Bourges (France), Esterline Advanced Sensors

uses a number of packages including SAMCEF®

for mechanical and thermal modelling

(in vibration conditions or in non-linear geometrical/material conditions) and

HYPERMESH®

(from Altair for meshing the parts). Following some years of using

SAMCEF®

, we are satisfied that it provides a good correlation between our test

measurements and provides a robust and high performance from the different

modules we use.

The current article is organised around three major experiences:

1- A brief presentation of recent Esterline Advanced Sensors’ developments

making intensive use of SAMCEF®

packages (an example per module is

presented)

2- How the high capacity of SAMCEF®

packages can be interfaced with external

tools throughout the modelling of a sensor, including a hyperelastic material

(through BACON® and SAMRES®

- modal analysis and dynamic response),

3- Finally, additional examples (some anecdotal) will be discussed : a way to

manage and launch multiple runs and to “automatically” plot, resize and crop

pictures in a post-processing stage.

3- Examples of Esterline Advanced Sensor modelling, performed using the SAMCEF ® package

3-1 Thermal modelling on an engine structural ring (THERMAL® module) Our objective was to determine the maximum temperature of the stud soldering of

the engine features (in terms of specific mass flows W, static temperatures Ts and

static pressure Ps of internal flow and secondary one).

After calculating “by hand” the forced convective heat exchange coefficients h

(D

Nuh

extint/

⋅= λ where the Nusselt number ( )PrRe,fNu = depends on Prandtl number

Pr and Reynolds one Re) inside and outside the ring as Boundary Conditions BC’s,




the Finite Element Analysis is performed in non-linear steady state condition (see

Fig 2-b and Fig 3).

Note no radiation has been taken into account in the current FEA.

(a) (b)

Fig 2 : Mesh (a) and thermal field (b)

(a) (b)

Fig 3 : Thermal field (zoom on the studs) and nodal values (cross section)

3-2 Thermo-mechanical modelling on sensor (THERMAL® and MECANO® modules) Our aim here was to validate the strength of the flange under fire conditions

(sensor on a hydraulic duct). The analysis includes the fire test conditions for the

thermal loading (flux, fluid temperature and heat exchanges) as well as the fluid

pressure and the tightening for the mechanical loading.

In addition to material non-linearity, contact conditions were implemented (.MDS

command) between the flange and a rigid plane (that simulates the wall duct) as

well as between the flange and the screws (.MCT command). The tightening at

room temperature was validated through an initial static computation using .MNT

command (plus .MCE + FRE1 command and .SUB + IREF 1 one).




(a) (b)

(c) (d)

Fig 4 : Mesh in BACON® (a), contact conditions (b) and thermal mapping (c-d)

The Safety Factor SF (SF = σequivalent / σUTS where σequivalent is the equivalent stress

in Von Mises meaning) is calculated in MECANO®

through XC keyword in the

.MAT command (see Fig 5-b). In addition we can note the tightening lost (minus

60 % between room temperature & max. temperature) due to the difference of

material expansion between the screws and the flange (i.e. difference of C.T.E).

(a) (b)

Fig 5 : Safety margin calculation (a) and tightening lost (b)




(a) (b)

(c) (d)

Fig 6 : Displacements due to thermal expansion (a to c) and plastic strain of

the flange (d)

3-3 Dynamic non-linear calculation (MECANO® module) At the very early stage of the development our Customer asked us to estimate the

force on four screws of an inlet sensor following a bird impact (see Fig 7). This

initial study required an elastic-plastic calculation to be performed (without

considering any strain rate effect).

The loading was considered as a Pressure applied onto the intrusive part in

transitory conditions ( VCP x2

21 ρ= - see Fig 8-a). The resulting forces in the 4

screws are plotted in Fig 8-b.

Contact conditions were implemented (.MDS and .MCT commands).




(a) (b)

(c) (d)

Fig 7 : Mesh (a-b) and Rigid surfaces (c) and Impact surface (d)

The forces are plotted thanks to .MNT command (see Fig 8-b).

(a) (b)

Fig 8 : Transitory scheme and resulting efforts in the 4 screws (.MNT command)




3-4 Modal analysis and Dynamic response (DYNAM® and REPDYN® modules) Modal analysis and dynamic response analyses are often performed to determine

the maximum stress, and subsequently, to calculate the Safety factor (from the

material fatigue strength or from the Goodman diagram).

The section 4 presents a more detailed example of modal analysis and dynamic

response.

3-5 Random vibrations on a pre-loaded sensor (ASEF® and DYNAM® / SPECTRAL® modules) Here follows an example of a sensor placed in cryogenic ducts (Hydrogen and

Oxygen liquids) and worked under high (random) vibration spectrum (see Fig 9) for

a short duration (600 seconds). The analysis was performed in two steps : a pre-

loading with ASEF®

(a mapping of the pressure drag) and random calculations with

DYNAM®

/ SPECTRAL®

(see Fig 10).

The results provide either σRMS and δRMS (where σ is the stress and δ the

displacement) or σpeak and δpeak for PSD’s applied in the 3 directions at the same

time (see Fig 10).

(a) (b)

(c) (d)

Fig 9 : Mesh (a), Pressure profile following the azimuth (b-c) and vibration

spectrum (PSD –d)

VCPP p2)(

2

1)( ∞∞ ⋅⋅+= θρθ




(a) (b)

Fig 10 : RMS Stress field with σRMS << σPeak (a) and RMS

displacements (b)

4- Interfacing of SAMCEF ® with Esterline Advanced Sensors’ external routines/modules

In addition to its robustness and its reliability, SAMCEF®

proved relatively easy to

interface with external routines. And, to illustrate this, below is a good example!

In this study, the sensor was suspended through an elastomeric damper i.e. hyperelastic

material (see blue sub-part in the Fig 12). The material is highly non-linear : indeed, its

stiffness depends on both the mass of the sensor and on the vibration spectrum (i.e.

mechanical loading). Fig 11 illustrates this particular behaviour well : Fig 11-a shows

that the transmissibility changes with the vibration spectrum as well as the natural

frequency and Fig 11-b shows resonance decreases of more than 40%, between 1g peak

input and 40g peak.

(a) (b)

Fig 11 : Test measurement : transmissibility’s in one direction (a) and

normalized resonance change




With 3 million D.O.F (Degree Of Freedom), the direct integration to take into account

the non-linearities (both material non-linearity and contact BC’s) is not possible. So, in

order to use the modal superposition method, our solution was to replace the elastomeric

material by springs (BUSH elements) with a different stiffness and a different damping

value in each direction (KTx ≠ KTy ≠ KTz and CTx ≠ CTy ≠ CTz where KT represent the

stiffness and CT the damping value).

Specific vibration tests were performed in order to isolate the specific behaviour of the

damper in vibration conditions i.e. to avoid any specific mode of the intrusive part (see

Fig 12-c – the mock-up has the same weight and the same centre of gravity CG) ; the

tests were modelled to fit the spring parameters (Fig 12-d and Fig 13). For that purpose

SAMCEF®

was interfaced with SCILAB [2] to manage the optimization process (non-

linear NELDER-MEAD simplex algorithm) as well as the recording of the intermediate

results coming from BACONPOST®

/FAC®

and SAMRES®

and the updates of the input

.dat files (see Fig 15 and Fig 16).

(a) (b)

(c) (d)

Fig 12 : Mesh of the complete sensor (a-b) and damper characterization

mock-up (c-d)

Based on the test measurement analysis, a strategy has been adopted to reduce the

number of variables from 14,000 to 12 depending on the node localization (see Fig 14):

1- The cost function has been defined as the Sum of the Square Errors (SSE)

between the resonance calculated by DYNAM®

and the measured ones to fit the

BUSH stiffness (see Eq. 1),

2- In the same manner the cost function is defined as the SSE of the displacements

for the fitting of BUSH damping values in REPDYN®

module (see Eq. 2).




( )∑

−⋅==

n

isfrequencie

F

FFWSSE

measured

measuredFEA ii

1

2

_0

_0_0

(Eq. 1)

Where

○ Wi is the Weight of the ith natural frequency

○ F0_FEA is the ith resonance calculated by

DYNAM®

○ F0_measured is the ith test measurement on the

shaker

○ n is the number of natural frequencies

( )∑

−⋅==

n

intsdisplaceme

measured

measuredFEA iiWSSE

1

2

δδδ

(Eq. 2)

Where

○ δFEA is the ith displacement calculated by

REPDYN®

○ δmeasured is the measured displacement of the

ith mode

The damper is replaced by BUSH elements with one end connected to the flange, and

the other end linked to the shaker node with the .LIA command (see Fig 13).

(a) (b)

(c) (d)

Fig 13 : Damper modelled with springs

(a) (b)

Fig 14 : Fitting parameters strategy depending on nodes localization




Fig 15 : Algorithm for fitting parameters (each update is performed thanks to Scilab)

* Case study No : X

* Gamma : 1 G

* Iteration No : X

* KG_X = 9.45225

* KG_Y = 6.98881

* KG_Z = 22.0209

* KS_X = 17.5172

* KS_Y = 54.706

* KS_Z = 17.1971

* CG_X = 0.000226055

* CG_Y = 0.000869445

* CG_Z = 0.00264304

* CS_X = 0.00113199

* CS_Y = 0.00138422

* CS_Z = 0.000223629

* Bacon 0 in progress .....

* Bacon 0 ended .....

* Dynam in progress .....

* Dynam ended .....

* The FEA is launched following the 3 axis !

* axis 1

* Repdyn 1 in progress .....

* Repdyn 1 ended .....

* Baconpost 1 in progress .....

* Baconpost 1 ended .....

* Samres 1 in progress .....

* Samres 1 ended .....

* axis 2









* axis 3









* Samcef displacements :

1. 0.0011229

2. 0.0005520

3. 0.0008592

* Measured displacements for 1 G:

1. 0.00112

2. 0.00054

3. 0.00086

* SSE = 6.66996e-005

Fig 16 : Example of a loop for fitting damping values on the displacements in REPDYN®

- Each file / update / run is managed with algorithms written in Scilab

(note the stiffness were initially fitted)

DYNAM® : stiffness’s � natural

frequencies + modes fitting

REPDYN® damping values =

displacements peak




(a) (b)

From 35G the changes have significant sliding

origin

(c)

Fig 17 : Parameter changes with the vibration spectrum (a-b)

The two tables below show that the Finite Elements Analyses correlate well with the

practical test results (see Table 1 and Table 2) : after performing the vibration test we

analysed the initial results (by adding further instrumentation we could record the

thermal increases due to the friction at the damper/flange interface) � the curves

inflection describes the conditions where the sliding become significant (see Fig 17-c).

Vibration Spectrum [g peak]

Mode 1g 5g 10g 15g 20g 25g 30g 35g 40g

1 0.08% -0.01% -0.11% 0.02% -0.24% 0.02% 0.08% -0.12% 0.17%

2 0.03% -0.04% -0.14% 0.02% -0.01% -0.17% 0.18% 0.15% 0.11%

3 -0.08% -0.11% -0.04% -0.10% -0.03% 0.03% 0.02% 0.01% 0.02%

Table 1 : Comparison of resonances between FEA analysis and actual measurements

Vibration Spectrum [g peak]

Mode 1g 5g 10g 15g 20g 25g 30g 35g 40g

1 0.24% -0.15% 0.05% -0.23% -0.14% 0.27% -0.87% -0.72% -0.56%

2 2.43% -0.77% 0.31% 0.53% 2.54% -1.31% 3.15% 1.67% 0.41%

3 0.05% -0.24% -0.04% -0.67% -0.47% 0.44% -0.50% 0.30% -0.73%

Table 2 : Comparison of displacements between FEA analysis and actual measurements




From the test vibration (i.e. in an inverse method) and based on the customer vibration

spectrum (see Fig 18), the stress mapping is calculated re-using the fitted parameters:

- Between input γ the parameters are linear interpolated,

- A complete run (DYNAM®

+ REPDYN®

) is needed per input γ

and natural frequency

The previous FEA’s are driven with Scilab.

Fig 18 : Example of vibration spectrum provided by a customer

The picture hereafter (see Fig 19) presents an example of the resulting modal analysis

(DYNAM®

) for an input γ coming from test results analysis.

(a) (b)

(c) (d)

Fig 19 : Example of modal analysis performed after fitting parameters




5- Miscellaneous 5-1 Multiple runs in batch mode

In the same manner as the previous example, it is possible to plan multiple runs, in

batch mode, from a Scilab file.

5-2 “Automatic” picture post-processing The pictures are generated from a script into BACON

®/ BACONPOST

® (.PLOT

command). Commonly dozens of pictures may be generated in a complex

modelling mode to present shapes, displacements, stress fields and so on. The

previous pictures can be easily resized, cropped and so on (using ImageMagick

libraries [2]) so that they’ll be included in a report, technical note or any other

document.

This is currently done in two steps. Firstly, a grid is superimposed onto the picture

giving the parameters (cropping) and, in a second step, the picture is cropped and

eventually resized (see Fig 20).

Fig 20 : Example of picture “automatic” cropping




6- Conclusion

SAMCEF codes are routinely used at Esterline Advanced Sensors to help reinforce the

quality of our products, with FEA’s performed at both the development and

qualification stages.

The initial work is undertaken to validate the strength of our sensors, followed by a

second phase to determine the safety margin or to explore conditions where physical

tests cannot be performed e.g. cryogenic conditions, very high frequencies, high

spectrum and low frequency (such as the fan blade off condition).

After some years of intensive use of the SAMCEF package, Esterline Advanced Sensors

has no reservations about the robustness, reliability and efficiency of this solution.

7- References

[1] Scilab webpage : http://www.scilab.org/

[2] ImageMagick webpage : http://www.imagemagick.org/script/index.php

Author Reference : paul.carrico “at” esterline.com

8- Thanks

Thanks to James Ewing (V-P Engineering and New Technologies – Esterline Advanced

Sensors) for his input and support.

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