HAL Id: hal-00509793
https://hal-mines-paristech.archives-ouvertes.fr/hal-00509793
Submitted on 9 Mar 2011HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
New Numerical Technologies for the Simulation of Arc
Welding Processes
Michel Bellet, Makhlouf Hamide, Christel Pequet, Patrice Lasne
To cite this version:
Michel Bellet, Makhlouf Hamide, Christel Pequet, Patrice Lasne. New Numerical Technologies for the Simulation of Arc Welding Processes. Proceedings MCWASP XII - 12th Conference on Modeling of Casting, Welding and Advanced Solidification Processes, Jun 2009, Vancouver, BC, Canada. pp.Pages 563-570 - ISBN: 978-0-87339-742-1. �hal-00509793�
NEW NUMERICAL TECHNOLOGIES FOR THE SIMULATION OF
ARC WELDING PROCESSES
! "#$ % # &'() $ * + * , -. / 0* -1 $+ $ * + * , 2 / 1 -3 45 6 5 2 * * 1 2 1 Abstract * * * * 5 40 1 * 5 2 4 - 5 2 4 2 2 * 5 2 7 . - $ 4 * 8 * 5 2 - + 1 . 1 -Introduction " 2 * 4 2 * 2 * 8 5 2 * 5 . - .7 1 6 • * 2 4 5 . 4 2 5 . * -• 5 1 5 . * 5 1 2 * . 4-• * * * . 4 2 * 1 . -9 1 .7 1 1 1 1 * * 0 5 2 * #+"$: ;- < . * 2 - 1 5 2 2 2 * 0 2 0 5 5 . * = 0(>-* * * . 5 2 * 46 o 2 * ? @ o o < 1 2
-Modelling of Material Deposit
< 5 . 6 A A A 1 A A . A =B>- < ** ** 4 .4 * 2 1 1 5 . - 4 7 6 ! "# $ %%& ' ( ) * + , , - ) %%&* ./$#."%
0 2 4 5 . * * 4 * 2 1 2 * , 0 1 4 * 2 * 4 * 5 * 4 , 0 2 4 * 4 2 2 * ? ! $ @-< * * 1 ** * 5 * * 4 5 4 5 - < * ?2 5 2 9 +:@ * 2 5 2 * * 1 . 8 2 5 5 * 2 2 - * * 2 1 5 * 2 1 . 5 7 - 4 ** 4 4 . .4 1 8 -* -* 1 * 1 5 ? 2 @- + ? 2 @- . 5 1 !* .46 ⌡ ⌠ − + ⋅ ∇ ρ θ ρ v ? @ 5 v 1 4 ρ 4
∑
= C θ 2 1 2 1 2 = 0> = (C > . 2 1 5 1 - . 2 2 1 5 * 5 4 2 1 . * * 5 7 -2 - $ 2 * 9 + 5 2-5 ** . 2 6 2 2 5 5 * * .4 . 4 * 2 5 * C ! . 2 - 5 * -2 2 * 2 2 4 . 4 * 2 1 4 - 1 4 1 2 1 40* = )>-* 2 6 v x x= +∆ ∆ + ? @ ; * 1 1 2 ? * * . 4 4 1 * 4 * * @ 7 5. - < 4 . 5 1 1 2 7 * ? * 2 1 D@-base metal weld joint elements affected by mass supply welding direction< 2 < 0 * . 1 ! 2 2 5 . ** - ! . 2 ? . @ ? * 4 7 @- C 4 * .4 2 5 2 1 .4 α ?α 1 E @- < α 2 A1 A FG * 1 4- α E0 4* ? @- < ** 4 ! 2 * 4 * * -1 s 4ρ ** 2 1 40* * . !* 6 ρ α ρ α ρ α α +? − @ = +? − @ = s s s ?(@ 5 * 1 4- < . 1 * . * . 4 χ - 1 ! Ω . .4 ! 2 5 5 6 E @ @? ? = ⌡ ⌠ + ⋅ ∇ − + − + ⋅ ∇ ∀ Ω χ α θ ρ ρ α v v ?B@ $ ! 2 5 1 2 * . - G * . 1 5 * .4 1 2 5 2 * E @ ? − ⋅∇ = + ∂ ∂ α α v v ?)@ 5 ∂ C∂ 1 5 * v 1 4-1 .4 4 09 =)>-1 . * .7 0 HH . 4 . ='>-$ $ * 1 2 * 5 * -* - * 5 2 2 - ! 2 5 . - 4 2 2 2 . 2 2 T . . !* 5 n n σn T= =− −γκ ?'@ γ 2 κ 1 ?* 1 1 ! 2 1 1 @ n 5 1 - . 5 1 5 6
∫
∫
∫
Γ Γ Γ ⋅ + ⋅ = ⋅ − I I I v n v n v T γκ ?&@ 2 2 * 5 .46 n n⋅∇ ⋅ − ∇ = ∇ ? @ ?J@ 1 .4 =&>6 n ⋅ ∇ = κ ?K@+ . ?&@ 4 * 2 κ .4 !* ?K@ =J>- ?&@ . 2 !* 2 !* !* . 4- " 5 2 * 0 * .46 @ ?∇ ⋅ ∇ = ∆ ? E@ * . 1 1 1 2 . 4Γ=K>6 n x x=∇⋅ ∇ =κ ∆ ? @ ? @ < 7 2 !* ?&@ 2 2 .4 * 5 2 6
∫
∫
∫
Γ Γ ∂ Γ Γ ∇ ∇ + ⋅ ∂ − = ⋅vI x vI x6 vI n γ γ κ γ ? @ 4 2 = E> 5 2 2 - < 2 5 * 0 * 2 5 1 4 v ? . *@- 5 2 6∫
∫
∫
Γ Γ Γ ∇ ∇ ∆ + ∇ ∇ = ⋅vI ? x@6 vI v6 vI n γ γ κ γ ? (@ . 2 4 * 1 4 * 1 . 4-2 - 2 9 + 5 2 ? * * @ 2 2 2 - G . . 2 5 * . * ? ! $ @- G 2 0 5 * 8 - < * 2 . ** 1 5 ! * ** 8 * -5 ? 2 2 FG 0 4* 2@ 1 . * * - + 5 2 ( * 5 7 * . * .4 5 2 2 -2 4 5 4 2 . 4 1 4 5 7 - * . ! .4 5-Control of Finite Element Mesh
9 1 * 2 2 .4 5 2 * * .
. 4- 5 2 = > *
1 2 * 1 4- 2 8
* . ** 0. .4
2 (- * . 5 2 2 FG 0 0 2 - @ * * 5 7 6 2 2 2 ? *@ 2 FG ?. @- .@ * * 2 ! . 5 . - @ +! * 2 1 * ? @- " 2 .@ @ 1 ? 1 $ . $ =
)>@-(
a H x a)
a x ! ! ⋅ ? @ ≤ ∈ ∈ ∞ ? B@ 5 H ! ? ! * 1 1 @ a ' 2 1 - 2 2 2 H 2 1 λ 1 λ - + 2 4 1 L ?5 @ 5 . 5 2 !* ** . 6(
)
5 { ! } ? @ !a Ma M H a∈ ∈ ∞ ≤ ⋅ = ? )@ 2 ** . * . . * . 2 1 * ε .4 2 6(
a Ma)
a∈ = ⋅ ∀ ∀ ε ? '@ < 5 . 4 ? ε@M- * 1 * .4 9 M * 8 = B> . .7 1 4 -! 2 ** . * . 0* 7 5 2 . 2 .4 1 2 2 5 2 .4 Axial coordinate [m] Te m p e ra tu re [ °C ] Transverse coordinate [m] A x ia l s tr e s s c o m p o n e n t σ88 [ M P a ] .@ @ @α
L
α
L E
1 7 - < 4 1
? * * @
5 2 .7 1 .
* 1 =( (
)>-Inverse Modelling for Identification of Heat Sources
< 0 2 0 2 5 2 * * 4 2 1 2 5 5 * 2 4 2 - 2 * 5 . 2 .4 2 * ? 2 * 2 5 5 2 * 2@- ; * = )> 1 2 4 2 . * 4 - * 8 8 2 . - 5 . 2 2 * .4 * 24 ** 4- < 2 1 4 . - 2 1 4 * . 4 * - < ! 5 1 ** 1 4 * 2 1 2 . 2 1 4-. * * 7 1 * 8 . 5 - 9 1 !* * 1 5 2 ? 4 1 2 2 ** 4 2 4 2 @ * * 2 1 2 * - ; 2 !* * * 2 * . 1 T!* T 1 . * - 1 * * q !* - 1 * . 2 q 5 2 Ψ?q@ . 8
∑∑
= = = Ψ !* @ 0 @ ? ? @ ?q q ? &@ 2 . ! . * 2 ! * 2 -< 5 2 * . * * 5 * * - : 1 5 Ψ * 5 !" Ψ Ψ# !* 2 5 5 !* ! * . . 5 * 1 4 5 5 !* ! * . 1 * 6 2 B- $ 8 ? N @ . ? . @ 1 5 1 4-∑
∑
= = = = − = Ψ − = Ψ !" # $ # $ !"?q@ ! ?q@ ?q@ ! ?q@ ? J@ < !* !" . 8 # . 0 . 2 2 B- !* . 5 . 8 5 2 1 6 =? + @C -. 5 2 !* base metal FZ − + − − + × = Ψ
∑
∑
∑∑
= = = = = = # !" $ # $ !" !* @ ? ! @ ? ! @ ? @ 0 @ ? ? @ ? O q q q q β β ? K@ 5 β 5 2 2 -8 * . 1 2 <G$G 5 = '>- 2 ) 2 1 ! * ** - * 2 9 + * - ( ' - 1 * . ?1 q@ 5 2 6 1 5 2 4 η ? * 5 1 4 4 @ 2 1 4 ! % 1 4 ε * 5 !ω? * . 2 1 5 * . 5 2 3 M ; .# 4 = &>@- * 8 BE ? % K' B / -J 9 8 9. #+ @ 4 2 * 1 . -2 )- +** 1 4 9 + 5 2 ( ' - @ * . 5 !* * 1 .@ 1 * 8 * !* 1 * 8 @ * * 1 1 5 5 2 * .4 -η % ε ω E-J) E J-) E- ) E-&E . 6 1 * -Conclusions " 1 . 1 * 5 .7 1 * 1 2 * 5 2 - # 2 2 * 5 2 2 5 5 * 1 2- < * 1 2 1 1 1 . 5 2 * 1 . 4 * - ; * 2 * 2 0 100 200 300 400 500 600 700 800 900 1000 0 50 Temps (s)100 150 200 Tc1: Numérique Tc2: Numérique Tc3: Numérique Tc1 : Exp Tc2 : Exp Tc3 : Exp calculated calculated calculated Temperature [°C] Time [s] @ .@ @2 1 2 - 4 1 4 5 2 24 * -References - - - A+ * ** 2 5 2 * A - < - - 2 2 : 2 + 1 $ G* -+- 9 - ? -@ M $ 4 ? EE'@ J))0J' - - - A+ * 1 * * . - +** 5 2 A - K < - - " < 2 2 + < 4 ? EE&@ )' 0 )'' (- - - - A+ * 1 0 2
5 2 * A & ' (' ) ' # ' *&+&+' &( ? EEJ@ ' B0'B B- - - 2 - # - "P Q A$ * 5 2 * A & ' (' ) ' # , *&+' BB ? KKK@ (E 0 ( ' )- R- A S * S !* . * 4 T A -;- 0 ? EEB@ '- G- A$ S 2 A -;-0 ? EE'@ &- R-%- . ;- - 3 - N A+ 2 A (' ' EE ? KK @ (()0()B J- - A< * 5 5 0
5A ' ) ' # ' *&+&+' & ? EE @ )'(0)&K K- $- 9 ;- R- % && & - $* 2 F 2 ? EEB@
E-$- 4 2 A+ 5 * * 5 A & ' (' ) ' # ' *&+&+' ) ? EE'@ ')K0'&
- - A S * * 2 A % . * / && , * / & ! & K ? EEE@ B'&0BJ'
- - ;S+8 1 - $ * AG * 2 8 2 2 A ) # )K ? KK @ ( 0(BJ (- - + 8 - 4 - 9 2 A+ * * # 4 2 0 4 . A - G +$ 2 * +** $ 2 2 EEB B- - 9 - * 8 A(; * 2 5 * A ' # ' ' # ' *&+' KB ? EE)@ BK) BK&' )- - A 2 U V A -;- 0 ? EEJ@ '-<-"- 2 1 9-F- 3 <-+- $-F- 3 * 8 1 A# . 2 * 8 24 <G$G 24A ) : 2 * F ? EE @ &-+- 3 - ; .# 4 A9 5 2 4
1 . * 8 A & ' (' 0 # & B& ? EEB@ )&K(0)JE' Acknowledgements