title: Etude physique et modélisation numérique du procédé de sertissage de pièces de carrosserie
text: + 38! :C " " 3 9 3 3 # E ε 4 6σ G 2 + 7 D F 2 3 3 3 @6 >C@ @B DA 3 3 3 JM 3 3 G G K I I M L M S $ # S $ # K L 3 3 + J 3 7 2 3 $' 6J 6 % 4 + 6L 6M 6K 6! 6 6N 3 7 3 5 3 6L 6M 6K! 6 3 6 2 7'@ 3 6N 6O "# $"# < 6 3 3,#J 3 2 6L6 6! 3 +.4././. D : 7 7 6 3 h3 3 7 3 3 6 = 7'O OW 81 3 38 6 7 " UJV 3 7 3 7 2 7 3 7'@ EL JG = D'3 L JG /'3 G 7 3 D! 2 2 7 3 D 6 3 3 7 1'3'38 7'UJV 3 3 := B 3 D 3 L JG 7 2 1'D E!'3 + 3 64 3 + 7'D 7 3 7 3 7 6 9 = @6 3 3 E F 5 6'>C@ @B #! 38 3 3 3 7 "? 7 3 7 38 6 3 3 3 7'7'77 ( 3 63 + 3 38 7 3 3 3 13 D, 3 R 3 6 3 3'3 3 h3 7 3 3 3 3 3 3 U V 7 3'7 3 6 (B " 6 X 7 6 4 7'' 3 3 7'D 6 ( = @6 @6@ @6 ULV 7 3 = 4 6 3 D! 3 3 + 7 9 *A6 4 DA J K 6 3 8'9 L 7'3 3 7 1M 1 :3 2 2 3 3 P 3'6 > 4 "? A >C@ @B F (B " C4 @6 A @. 9 3 3 6 77 ( 38 ULV6 UMV E 3 9 3 D 3 8 JL 8 9 3 3'3 3 37 3 7 3 B 9 = @6 6 F 7 6 I0G 4 I4G * 44 B6 6 : A= A :@A A B J"K 2 3 8 38 38 9 64 I4G I0G + 6 9 = @6 P $ 6 7'$ 7 6'7 9 3 3 38 D @'JG 3'U V +'J P 3 7'P3 3 3 3 > P + @6 A C9 A 3!$ $* 8 9 3 38 343 $ #! 34303 B, 3 7 5. $ 7 6! 1! 2 $ 3 3 2 @ $! 1 3 7 E @ E = E + E! E! 4E 6 38 E= J EL G (2 (< ) + 2 3 7 E 7 <6 3 31 (< )) 7 3 @ EL LG 1MJ1 > 4, 3 3 "? A >C@ @B F 3 6! 38 F :3 2 F= ν E + J +ν 7 " 9? @ ( ) EL MG F 3 B 7 6 3 64 : E J− ν 4 3 77 3 + 6 9 = @6 3 6 3'2 X & 3 @ σ σ F= EL KG σ 4 (σ 6 σ 6 σ, ) 3 3 3 3 6 7 3 7 3! 7 7 ε4 = L 2 7 3 E! @ E!. 3 @ EL G 7 3 2 E c G@ ε4 =! ε4 τ 3 3 38 EL G 7 3 7 + 2 7 38 2 38 3 3 3 3 E 6 7 L
  
  LG σ ε4
  
  
  
  = ε4 + ε4 −ε4 ε4 & ε4 ε4 ( (B "" C9
  
  6 @6 C9@
  
  @
  
  6 4 & DA CDA 7 1M 1 6 :A A C ε 4 6 :@6 6 A6 = J K > 4, "? A 3 3 6 3 3 3 7 3! 7 > >C@ @B 2 2 7 3 3 3 F'6 9 = @6 64 2 3 7 3 6 3 7 3 3 3 38 B 7 3 3'7 9 - 3 @ 9 = 9 (F 8 + 8ε 4 8ε 4 ) = σ (F 8 + ) − σ (ε 4 8ε 4 ) σ EL NG 3! 38 F 3 + E 3 σ 8'73 3 9 3 G +'3 3 3 7, 3 4 3 E3 7 2 7,'3 3'7 6 σ 2 3 1 3 6σ G 7 7 3 3 +'8 7 3 + 3 7 3 3 3 7 6 3 9 < E 9 = G6 2 3,9 2 2 3 9 77 3 38 2 7 3 LM 9 @ 9 < 9 = 3 7 3 9 < 3 9 3 8 2 3 3 2 3 3 G + 3 + 3 9 3 3 E3 38 @ ε4 =! @ ε4 > 9 = 9 = $3 9 = 9 <, 38 σ EL J G @ ε4 = 9 = 9 = EL OG EL JJG 9 < σ σ 9 < F F F F F F σ σ (B "% 4C 6 σ σ @6 6 @66 1ML1 A: *C: @A σ 6 4 DA > 4 $ 7 6 "? 3 + 3 EL J G 3 3 3 6 F 6 9 = @6 7 3 8 89 38 3 2 34343 7 2 7 3 3 '! 3 7 7'38 38 3 EL NG C 7 3 %" / 3 8 6 8 3 9 7 D 89 7 3 3 6 3 3 9 EL JLG 3 3! 38 F 7
  
  2 @ : (F ) J L + 3 EL JMG 7 3 @ : (+ ) =, 3 EL JKG 7'σ = L ( C @ : (F ) J L =F− 7 3 7 JOJL 3 7 3 σ /.+.+.). >C@ @B ∂9 ∂F E! = λ + A 7 3 9 38 7 EL NG6 3 9 @ − +)? ( − +) EL J G 1MM1
  
  > 4 / 2 "? 3 3 9 62 2
  
  @ σ (F 8 + ) =
  
  3
  
  3 J [(α F 6 9 = @6 64 B 3 8 38 9 9 3 T=F−+ << − α ;; ) + (α == − α ;; ) + (α == − α << ) + α =< + α <; + α =; 3 ( 6 8 7 >C@ @B 53 76 3W 121'3 $ 3 EL J G, A 3 3 6 )] EL J G 9 = 6 3 3 @ λ =ε4 EL JNG /.+.+.+. 0! 3 "'( L6 7 9 2 D 3 D + 3 9. 7'7 3 h3 3'J 2 9 E76 =6 JG 3 9'3 +6'' 7 > σ (F6 + ) = ( (α << − α ;; ) + 6 47 3 D 3 3 8 7 E76 =6 JG E c SG6'= 3 " JOMN UJV 3 3 7 3 9 8 @ (α == − α ;; ) + (α == − α << ) + ('( L6 4 E c O SG D 3 6 3, 8 3 F 3 α <; + α =; + α =< EL JOG 4T = F − + 7 - 8 89 4 (6 7 3 6 6 38 6 9 3 σ (F6 + ) = 3 3 D 6 6 $'6 7 7 @ ( + )α == 3 + (( + )α << − 3 3 3 (6 6 6 9 7 3 α ==α << + α =< EL G EL J G6 3 77 3,6 %)6 2, 7
  
  '(L@ (= O (J + ) 6 = J 6 J+ = J+ 6 1MK1 = (+ (J + MK ) EL JG > 4 "# 3 9 "? A >C@ @B " MN F 6 9 = @6'64 B 7 3 9 @ σ (F 8 + ) = L ( − +)?? ( − +) EL M 4 JJJJ = = LLLL = L L L ( ) + (( + ) JJ = JJ =− JJLL = LLJJ =− LL = LL (( + ). 7 (= +'3 EL JOG 3 3 =
  
  3 9 3
  
  8 " 7 3 3 3 JLJL = LJLJ =− L L = L L =− / EL LG L L = MK = O = J) 6 C D'+')
  
  3
  
  U V
  
  3
  
  '"
  
  # 3'"# 6(?! 3 9 3 9 3 UNV6 UOV6 UJ V 3 77 3 6 3 9 U 0686 V;W 3 9 " MN 3 9 D 6 3 EL NG +'7 L'/ 9 UKV6 U V $ σ (F6 + ) = ( 3 UKV 3 9 U V ( + 7 D 3 9 ( +! " 7 L 3 8 3 =− " D " 7 J J EL J G + 3 9 " MN 3 9 3 = EL MG 2 3 9 J J L = /.+.+./. ( L 3 J = 6 += = @ =− ( L 3 9 EL JG @ 9 3 G 3 2 3 @ J ( 5J + 5 N + 5J − 5 N +( − 1M 1 ) 5 N ) J N EL KG > 4 5J = J (α 9 3 77 3 6 8 3 6 7,6 3 Ψ= Λ= + 3 C 3 3 9 7 3 7 (γ α J == B 2 2,6?. ( Γ+Ψ N 3 1''2 3'3 M 77 UNV6 UOV6 UJ V + 7 3 J %)6 3 / σ (F6 + ) = 64 2 L 3 J 6 9 = @6 EL 3 7 F + ( α =< ) 6 3 Γ= >C@ @B + α << ).3 ( A α == − α << 5 = + == "? N 3 7 3 G 3 3 3U?? 4AAA V8W 3 9 3 9 + Γ−Ψ'3 9 ( 3 + @ N +( − ) Λ N ) J N EL G + γ α << ) ΨJα == − Ψ α << λJα == − λ α << + (ΨLα =< ) EL NG + (λLα =< ) 9 γ J 6 γ 6 ΨJ 6 Ψ 6 ΨL 6 λJ 6 λ 6 λL 7 2 1'3 6 3 77 3,6 %)6 2, 3 1'+ 9 EL G EL NG < < J6 3 3 7 3 3'7 3 38 3 / 2 7 ( UJJV 3 7 3 6 9 2 3 13 3 UJ V 3'3 9 5 8 3 7 3 38 / 3 3 3 9 3 3 C 3 9 D 1M 1'3 > 4 "? 343 3 A >C@ @B 6 9 = @6 64 B >$ # /.+./.). + 3 9 UMV + F 3 7 3 2 # 3 7 38 3 D 3 3 + 3 1 3 3 7 3 + 3 38 3 9 32@ 9 = σ (F ) − σ (ε 4 8ε 4 ) σ (ε 4 = 8ε 4 = + 7 3 7 3 EL OG )= EL L G 38 3 3 3 σ 67 3 3 3 3 7! 7 3 3 3 UMV6 UJLV6 38 7 3 8 3 8 7 3 3 3 σ (F ) 3 38 3 9 3 3 9 C 3 7 3 3 3 UJKV6 H 3 LK 31 + 7 38 + 3 3 3 7 3 3 7 3 7 3 G 3 2 3 7 + 2 + 3. 7 2 3 UJMV6 E 3 3'3 3 2! 7 7 3 3 3 3 1 3'EL J G 3 3 σ L 7 3 2 38 σ E G F J ε4 σ 6 K 6J 6JK 6 1J 7 3 38 2 c σ 1 σ 1L I0G I4G (B ") 4 C 6 @6 *C: @A B @ @4 6 4 6 *CDA @6 : F!Q, I0G 6 : @60:@ 4 @6 A6 = I4G 6 @ C 6 4 * 99 & A :> 6B 6 4@ 6 C A! 1MN1 > 4 - "? 3 A >C@ @B 3 3 3 3 F 3 ( 38 77 6 9 = @6 64 B 3 7 D 7 3 3 6 3 G 2 3 E /.+./.+. 3 2 + # 7 3 3 3 GE 3 "! 38 3 9 + 3 E L KG 7 3 1 3 3 7 2@ 9 = σ ( − +) − + 3 3 3 3 3 3'3 3 C38 3 3 6 77 3'EL LJG 2 7 3 3 38 3 3 / / # 2 $ 3 7 3 3 38 3 U V@ 38'9 >$ 6 3 R 3 3 9 3 2 3 3 9 3 "# + $ R!8 2 UJ V 3 77 3 3, + 3! E @ 7 += E! L 3 1'3 3 EL L G 9 3 5 77 3 1'3 2 ε4 + (ε − + 3 4 7 3 3 3 3 3 8 8 3 σ 2 3 4 < ε 4 < εJ EL LLG 4εJ < ε 4 EL LMG 3 7 P3 3 3 7 3 3 38 9 + 3 1'7 3, 3 3 9 3 3 @ − εJ ) 3 7 3 3 εJ 7 3 σ =− 3. 7 σ= 3 9 L 6 3 3 6 + 7 3 3, 7 77 ( 1MO1 38 K 38 3 > 4 96 2 εJ "? A 73 3 3 2 F 6 9 = @6 3 3 9 3 3 + 3 7 >C@ @B 2 3 B 3 3. 3 UJ V 3'3 77 3 4 U V6 UJ V 64 7 7 8 E G L 9 C, 7 σ σ L 7 3 2 F 38 + E G εJ J 6 K ε4 6J 6JK 6 1J 7 3 38 2 c 1 σ σ 1L (B "+ I0G @6 *C: @A : F!Q, I0G 4C 6.3!8 28 / >$ #! 9 38 UJOV 2 $ 3 + 77 += L I4G 6 4 6 *CDA I4G B : 6C DA 6C B 6 : @60:@ 4 @6 A6 = "# $ * 3? UJNV6 3 3 X 3 3 5 3 39 3 77 3, $ P3 3 σ =− 7 EL LKG! σ= 3? UJ V UJNV @ E! − γ ε 4 + 4γ 9 3 (. ( 2 3 1'3 P3 + + 3 9 3 σ 2 [− J + ( 7 3 3 4 < ε 4 < εJ E ] − =4 −γε J!) =4(− γ ε 4 − ε J!) 1K 1 9 6 4 γ 52 3 [J − =4(− γε )] γ @6 4 ε J < ε 4 E3 @ 3 G EL L G G EL L G > 4! 7 3 3 E A >C@ @B L 6 3 3 7 3 K 38 3 9 38 6 $ "? 7 F 6 9 = @6 64 B 7 3 3 P3 3 3 38 3 9'3 G σ σ L 7 3 2 F 38 + E G J εJ 6 K 6J ε4 6JK 6 1J 7 3 38 2 c 1 σ σ 1L I0G @6 6 @66 *C: @A : F!Q, I0G :@ 4@ 6 (B ". 4C 6 4 6 *CDA @6! 3 6 3 2 I4G B : 6C @: C 6 DA : @60:@ 4 3 3 C 2 7 6 Z 2 3 7 77 ( 3 3 38 77 6'3 3 / 7 2 /.+././.,!8 3 3 9 38 U V 3 1'3 3 " 3 6 73 9 6 I4G 7 $ 7 6 7 > 96 6 9 3 77 3 9 7 U V6 UJ V! 3 3 Y > @:> @6 A6 =, 4 3 C38 7 2 3 8 U JV + 3 #! " 8"! 3 7 3'9 = σ ( − + ) − σ (ε 4 ) 3 9 7 3 3 @ 9 38 3 4 EL LNG 1KJ1 > 4! 3 "? A >C@ @B F 6 9 = @6 7 + 3 3 3 7 3 + 3 # 2 3 3 X 3 3 3 @ EL LOG 3 EL LKG @ 3 23 )ε 4 − EL M G 3 77 3 3 3 3 3 3 c 2 6 2 < 3 @ σ (ε 4 ) = (ε ) [J − =4(− + (ε ) = 4 38 38 EL LKG + 4 4 3 38 (ε ) 3 $ 3 3 2 σ C ( 7 3 σ 9 + 3 + + = 3 (. ( V4AW 3 3 σ (ε 4 ) = 38 3 7 2 B 3. $ +'9 7 7 3 3 3 64 4 3 EL MJG 2 38 3 " EL MJG G + ε 4 )] 3'3 3 3 3 31. 3 D 3 σ (ε 4 ) = 5ε 4 6 (ε ) = 5ε 4 $ 6 4 EL M G − 3 3 3 1'3 31 7 3 7 σ = σ (ε 4 ) + 3 3 3 [− J
  
  + ( ] − =4 −γε J!) =4(− γ ε 4 − ε J!)
  
  1K 1 6 P3 @ 4 γ 1'3
  
  [J − =4(−
  
  γε )] γ σ = −σ (ε 4 ) + E @ 4 < ε 4 < εJ EL MLG 4 εJ < ε 4 EL MMG > 4 + 7 LN "? A >C@ @B 3 F'6 9 = @6 3 7 3 38 3 2 3 13 + 3 7 3 3 77 3 3 3 6'3 1'E 3 3 1'E 3 3 3 3 3 77 ( 38! 6 C D 7 C38 3 7'3 3 D ( U MV + 3 77 3 3 9! 9 9 5 8 64 B 3 3 6 9 1'3 6 3 G $ 3 EL MLG EL MMG 6, Z2 1'G 1 ', 38 8 U V6 8 U LV6 :3 2 3 U KV 7 σ L 7 3 2 F 38 σ E G J + ε4 σ 6 K 6J 6JK 6 1J 7 3 38 2 c 1 σ σ 1L I0G (B "/ 4 C 6 @6 6 @66 *C: @A B = *CDA @6 : F!Q, I0G 6 : @60:@ 4 @6 A6 = 4 @ A: C * 99 & A :> 6B 6 4@ 6.3! 3 # 2. 3 4 4 3 4εJ < ε 4 8 EL M G 3 EL MNG J E G 3 2 [ 9 3 1'+ 3 77 3 $ 38 6 3 3 3 3 77 ( 38 + 7 LO 31 3 P3 1'77 3 77 3 [ C 7 9 C 8 9 3'7 3 3 8 4 (ε )
  
  = (J − β ) (ε ) (ε ) = β (ε ) − β (ε ) σ (ε
  
  )
  
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