7th International Symposium on NDT in Aerospace – Tu.3.A.5

1 License: http://creativecommons.org/licenses/by-nd/3.0/

DATA ASSIMILATION FOR MONITORING RESIN TRANSFER MOLDING OF COMPOSITE

MATERIALS

Ryosuke MATSUZAKI 1, Akira TODOROKI 2, Masayuki MURATA 2, Masaya SHIOTA 1 1 Tokyo University of Science, 2641, Yamazaki, Noda, Chiba, Japan

2 Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro, Tokyo, Japan E-mail address: rmatsuza@rs.tus.ac.jp (R. Matsuzaki)

Abstract

Vacuum assisted Resin Transfer Molding (VaRTM) is widely used for molding of composite structures. However, ensuring complete impregnation of the resin into fiber materials is difficult and it sometimes causes the formation of un-impregnated regions, called dry spots. Due to the poor quality of a VaRTM process, its application is currently limited. Therefore, monitoring of the resin flow during the process is necessary to predict and prevent the formation of dry spots. This paper presents a method to observe resin impregnation in a VaRTM process without embedding sensors into composite structures. Planar-shaped sensor electrodes arranged on a molding tool are used to measure electrical capacitance values from pairs of the electrodes. These measurements are combined with the numerical simulations of a VaRTM process to estimate the state of the resin impregnation. This method is based on the ensemble Kalman filter (EnKF), known as a sequential data assimilation technique. The proposed method was examined by a numerical experiment. In the numerical experiment, the resin-impregnated region and the permeability distribution of a fiber preform were estimated concurrently and it was confirmed that the decrease of flow velocity in a low permeability region could be estimated.

Background

Ø Low  cost  molding  method  

Molding  tool

GFRP  

Dry  fabrics Vacuum  bag

Molding  toolVacuum  pumpResin

Resin  impregna>on

Dry  fabrics  100mm

u VaRTM  (Vacuum  assisted  Resin  Transfer  Molding)  

Monitoring  of  resin  flow  is  necessary.

Ø Quality  problem  

Fiber  preforms  are  stacked  

Dry  spot  (Region  uncovered  with  resin)  

Embedding  sensors  in  composites  may  affect  on  material  strength.  

Flow  direc>on  

Op>cal  fiber  sensor  etc.  

Measurement  range  is  limited  to  small  area  near  the  sensor.  

Measurement  instrument

Resis>ve  sensor  etc.  

Resin

Resin  inlet

Measurement  instrument

Recent  studies  for  flow  monitoring

Exis>ng  sensors  are  not  suitable  for  monitoring  of  thick  part  processing.

Invasive sensing Non-invasive sensing

2

Data  assimila7on  for  flow  monitoring

non-‐invasive  capaci>ve  measurements  

Stochas>c  simula>on  of  resin  flow  

Integra>on  

u Requirements  for  flow  monitoring  of  thick  part  processing

Ø Proposed  method:  data  assimila>on

・  Non-‐invasive  sensor  ・  Applicability  to  three  dimensional  resin  flow  monitoring  

Sequen>al  data  assimila>on  by  the  Ensemble  Kalman  Filter  

Conflic>ng  with  each  other…

Objec7ves

Development  of  3  dimensional  resin  flow  monitoring  method  by  an  approach  integra>ng  sensor  measurements  and  numerical  simula>ons  

Ø Proposing  a  sensor   that  can  obtain   the   informa>on  of  three   dimensional   resin   flow   from   a   surface   of   a  structure  

Ø Developing   a  method   to   es>mate   resin  flow   from   the  measured  values  and  numerical  simula>on  

Ø Inves>ga>ng   the   validity   of   the   proposed   method   by  numerical  experiments  

3

Overview  of  the  proposed  method

Three  dimensional  resin  flow  is  es>mated.  

(1)  Capaci>ve  sensors

Sequen>al  data  assimila>on  by  the  (3)  Ensemble  Kalman  Filter  

(2)  Stochas>c  simula>on  Uncertainty  in  a  VaRTM  process  is  simulated  by  

using  mul>ple  simulators.  

u Flow  monitoring  by  an  approach  integra>ng  electrical  measurements  and  numerical  simula>ons

(1)  Electrical  capacitance  sensor

A  vector  ct  provides  informa>on  about  3D  resin  flow.    However,  insufficient  to  reconstruct  the  resin  distribu>on.  

Molding  tool

Glass  fabrics

Electrical  capacitance

Electrodes

u Mul>ple  electrical  capacitance  measurements

c1

c2

cM

Resin

Resin  distribu>on：  N:  No.  nodesfi  :fill  frac>on  (0≤  fi  ≤  1)  

Resin  flow  represented  by  f

( )TNt ff ,,1 !=f1

0

0.5

Change  with  resin  flow

Capacitance:M:  No.  measurements  

( )TMt cc ,,1 !=c

Inversion  

(2)  Stochas7c  Simula7on:  Part  1(i)  Simula>on  of  homogeneous  model  

p∇−=φµKu

Darcy’s  law  u:  Resin  velocity,    p：Pressure  　:Porosity,    μ：Viscosityφ

(ii)  Simula>on  of  inhomogeneous  model  

Permeability  is  spa>ally  constant.  

Resin

{ })(1)( xKxK α+=Spa>al  varia>ons  of  permeability:  

Low High

x:  Posi>on  

x

z y

Ne:  number  of  finite  elements  

( )TNe,,, 21 ααα !=αPermeability  distribu>on  vector  

Permeability  is  not  uniformly-‐distributed.  

Discre>za>on α(x):  Devia>on  

K：Preform  permeability

(2)  Stochas7c  Simula7on:  Part  2(iii)  Stochas>c  simula>on  of  inhomogeneous  model

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧ −

−−

−−

−=z

ji

y

ji

x

jiji

zzyyxxCov

ηηησααα exp),(2xx

ηx, ηy, ηz:  Correla>on  lengths,  σα:  Spa>al  varia>on  

⎟⎟⎠

⎞⎜⎜⎝

⎛=

)(0

)(0)(*

0 l

ll

αf

f ft:  Resin  distribu>on  αt:  Permeability              distribu>on  

Ini>al  state  vectors  

α(xi) α(xj)

xzy

Samples  of  permeability  field    

Assuming  a  covariance  func>on  of  the  devia>on  α(x),  samples  of  spa>ally  correlated  permeability  distribu>on  are  generated.  

1.2

0.8

1.0

1+α{ })(est0)1(est0 ,, Lαα !

),,1( Ll !=

),,1( Ll !=Stochas>c  simula>on  

)( )*(1)*( l

tl

t F −= ff

u Darcy’s  law  

u Con>nuity  equa>on   u Advec>on  equa>on  of  fill  factor

0=⋅∇ u

0)( =⋅∇+∂∂ ftf u

Numerical simulation of VaRTM

⎪⎩

⎪⎨⎧

=ally  filled  

：Filled

f:  fill  factor { } { } 0][][ =+ PKfCdtd

u Finite  element  method  

VaRTM  simula>on  

Computa>on  of    pressure  distribu>on

Update  fill  factor

Fin.

Ini>al  condi>onK: permeability  tensor  u:  velocity, P:  pressure  　:  porosity, µ:  viscosity

P∇−=φµKu

φ

ft+1true

True  resin  distribu>on  

Δct        Measurement

(3)  Ensemble  Kalman  Filter  (EnKF)

Ensemble  Kalman  Filter

ft-‐1*est(1)

ft-‐1*est(L)

Ø Update  ft  and  αt  by  measurements  ct  

u Flow  monitoring  integra>ng  simula>on  and  measurements

　ft*fore(1)

ft*est(1)

fttrue

ft+1*fore(1)

t-‐1 t t+1

Δct+1

　 　ft+1*est(1)

Es>ma>onsFiltering

Predic>on

Predictonft*:  State  vector,    

Stochas>c  simula>on

)( )(e* 1)(f* l

tl

t F −= ffEs>ma>onForecast

L  independent  simula>ons  

Observa>on  equa>on

noise.)( true += tt h fc

h:  Observa>on  operator  St:  Sensi>vity  matrix  vt:  Observa>on  error  vector  

!

!

ft-‐1true

tf)f(f )()( vffSf +−+≈ t

lttth

⎟⎟⎠

⎞⎜⎜⎝

⎛=

)(0

)(0)(*

0 l

ll

αf

f

F:  Simula>on  operator  

　Numerical  experimentsForward  simula>on Es>ma>on  by  the  EnKF

x

zy

Resin  inlet

),,1()(*est1 Lll

t !=−f

)( )(*est1)(*fore l

tl

t F −= ff

)( )(estmsr)(*fore)(*est ltttl

tl

t ccGff −+=Gt：Kalman  gain  

3015 180

Low  permeability  region,  0.3K0

x

zy

Resin  inlet

unit:mm

Glass  fabrics,  K0K(x)=K0[1+α(x)]

Ini>al  ensemble  No.  members,  L=80

1.2

0.8

1.0

1+α

},,{ )(0)1(

0Lαα !

Resin  flow:

},,,{

},,,{msrmsr

0

truetrue0

!!

!!

t

t

ccff

u Finite  element  simula>on

No.  elements:  4608  No.  nodes:  5625  

No.  measurements:  36  

Ensemble  forecast  

Update  Capacitance:

3015 180

x

z y

unit:mm

(a)  Center

(b)  Front  side

3015 180

x

z y

1.0

0.3

Forward  simula>on Es>ma>on  by  the  EnKF

True  :  fttrue Es>ma>on:  Flow  front ∑=

=L

l

l

tt L 1)(estest 1 ff

Resin  inlet

Results  of  resin  flow  es7ma7on:  (1)

(a)Center

1.0

0.3

True  :  fttrue Es>ma>on:   ∑=

=L

l

l

tt L 1)(estest 1 ff

Forward  simula>on Es>ma>on  by  the  EnKF

Results  of  resin  flow  es7ma7on:  (2)

(b)Front  side

Resin  inlet

Flow  frontDecrease  in  velocity  in  a  low  permeability  region  could  be  es>mated.

0.3 1.00.4 0.6 0.8

1+α

Results  of  permeability  es7ma7on:  (1)Forward  simula>on Es>ma>on  by  the  EnKF

0.3 1.00.4 0.6 0.8

1+α

Results  of  permeability  es7ma7on:  (1)

Cross-‐sec>on  z=-‐15  mm

Top  view    (z  =  -‐15  mm)  

Results  of  permeability  es7ma7on:  (2)

0.3 1.00.4 0.6 0.8

1+αPermeability  distribu>on  was  es>mated  simultaneously.

Conclusions

Ø Flow  monitoring  method  integra>ng  electrical  measurements  and  numerical  simula>ons  by  the  EnKF  was  developed.  

Ø In  a  numerical   inves>ga>on,   it  was  confirmed  that  the  resin  flow  front   and   permeability   field   can   be   es>mated   during   a   VaRTM  by  the  proposed  method.  

Measurements   Simula>on  

Bridging the gap between measurements and simulation

Data  assimila>on  (EnKF)