NUMERICAL SIMULATION OF KEYHOLE SHAPE AND TRANSFORMATION FROM PARTIAL TO OPEN STATES IN PLASMA ARC WELDING

Ö 7 Ö Vol.7 No. 11 Ö Ö È ACTA METALLURGICA SINICA Jun. 11 pp. ÐÅÔ ÎÔ Ê Đ 1,) 1) 1) 1) ß ÍÊ ½ Ñ٠ؽÁ, ÔÒ 51 ) ß Í Ñ ß, ÔÒ 511 µ² Ç Æ Đ, ÅËÀ Ð Ï (PAW). Â, mm É PAW» ½ËÁ ÕË, Ë Ð¹ ²Á»¼Á Î. µ²» Ǽ, PAW È À ¹ ½Ë, ÕËË ³ÆÕ Ç. Î ÅÛ, ³Đ Æ ; Ì Ì± Ó Õ ¹ ÐÀ ¼ ÅÛ ; Ð ÏÇ Ó Ð ³ĐÕ ÅÛ. À PAW Ź ¾Â, Á ÕË ½Ë¾ÂÂ. Ï À Ð Ï Å,»¼, Ç Æ, Á Ö TG5. Å Ú A à 1 191(11) 7 NUMERICAL SIMULATION OF KEYHOLE SHAPE AND TRANSFORMATION FROM PARTIAL TO OPEN STATES IN PLASMA ARC WELDING HUO Yushuang 1,), WU Chuansong 1), CHEN Maoai 1) 1) Key Lab for Solid Liquid Structure Evolution and Materials Processing (Ministry of Education), Shandong University, Jinan 51 ) School of Materials Science and Engineering, Shandong Jianzhu University, Jinan 511 Correspondent: WU Chuansong, professor, Tel: (531)39711, E-mail: wucs@sdu.edu.cn Supported by Key Project of National Natural Science Foundation of China (No.5933) Manuscript received 11 1 7, in revised form 11 3 1 ABSTRACT It is of great significance to develop a mathematical model of keyhole shape and dimension in order to widen the process parameter window and improve the process stability in keyhole plasma arc welding (PAW). In this study, a keyhole model was developed according to the force balance conditions on the keyhole wall. The establishing process of quasi steady state keyhole was numerically simulated for stainless steel plates of mm thickness, and the keyhole shapes and dimensions were obtained under different welding process parameters. The transformation mechanism of the keyhole from blind (partial) to open (complete) states in PAW process was analyzed based on the calculated action forces on the keyhole wall. The values of action forces at different locations on the keyhole wall were calculated. With increasing of welding current, the keyhole depth rised in a nonlinear way. There existed a critical value of welding current, i.e., if welding current was a little bit higher than this value, the keyhole inside the weld pool would suddenly transform from partial state (blind keyhole) into complete state (open keyhole). The fast centralization of the plasma arc force at the keyhole bottom region resulted in the sudden transformation from a partial keyhole to an open keyhole. The keyhole PAW experiments were conducted to validate the numerical analysis results. KEY WORDS keyhole plasma arc welding, keyhole shape, force balance equation, numerical analysis Ñ «(PAW) ¼ ÍÇ * Ø ±Ù Ñ 5933 : 11 1 7, : 11 3 1 ÆÞ : ÔÅ, Ø, 1973 µ, DOI: 1.37/SP.J.137.11.1 Ô Ê, Æ ¼, ² Ò Ñ Ú, «¾ É «º [1,]. ¼ ÁÔº ± PAW º., Á PAW, ± Þ, «º Æ, É

Ö ÓÄ : Î º»À À Æ 1 «Ó Ê Ã «³Â«ÝØ ± [3,], Ì º ºÉ ¹ Ê. Ì Á PAW ¾º ³Â Â, º Ø Â Þ, Đ Æ Æ «º ³ÂÒ± ¼½ Ü ÞÊ. Á PAW, ± ¼ Ͳ, ÂÖ̱ ¼½ Ͳ Å. Keanini  Rubinsky [5] ÖÌ Ì PAW ºÂ º, ± ¼½ Ù ³ à ÛÞ. Fan  Kovacevic [] Û²Ñ Þ Gauss Þ, VOF(volume of fluid) ÖÌÌÜ Þ¼³ ¾±. ÁÈÂͺ Á [7] ± Đ¾ Þ PAW º ¾Ì, ± ± ¼. Metcalfe  Quigley [] ³º Á È ÐÇ, Á ˱ Þ ¾Ì, ± ± ¼½ Þ., Í ÔÜ ± Ñß ± ¼½ ¾Ì ± [5 1], Í º. º [13] ¾ Ñ ºÂ º Â, à Level Set Ñ ÞÚ Á ¾Ì ÕÖÌ, Ì Ñ Þ ³ ¾ Ò± ¼½Â Ï Ð Â³, ± Ñ Ð «. ³ ± È ÐÇ, Æà PAW б ¹, Á PAW ± ¼½Â Ï ¾Â ÖÌ, Ò Ã ¾ Æ. 1 ßÌ Þ Á PAW ««Ò± Ü. «¼½Â ÏºÞ ± ¼½  Ï, ± ¼½Â Ï ¼½Â Ï. ÍÞ PAW º, ¼ ÌÍÞ. Ô Õ¹ Ì ÍÞ¼½Â Ï ±. Æ º : Ï ÞÌ ¼½  Ï, ÞÒ ± ¼½Â Ï. Á PAW Â, º [9,1] ¾ Á PAW Æ Ú, ÆÌ Í Ã Þ ¹, Õ ÕÖÌ PAW ¼½Â Ï. ± ¹ ÖÌ ¼½Â Ï. ÆÚ + Ý Ã Þ ¹ Á PAW. Þ ¹, «¼½Â Ï [9,1]. Ó É ºÂ, Þ PAW.1 «ÕÂÛ ØÜ Ë Á PAW Ë, ± È ¼. Ø 1 ± Ô Ë È «. Ñ ³ Òº Ú ÜÚ Æ, x ³ «, z ³ º Ê. ±, ÒÑ Â, Í Ñ È p a, È p s (p s = ρgh, ρ, g ²ÈÚÊ, h ), «È p σ Â È ( Å È p r ) ¼Ñ., p a Ë ± ¼ Đ È, p σ  p s Ë ± à È. Ð Þ ± ¼ Ë, ± Í Ó²È ÐÇ. ± È ÐÇ, Ù : p a (x, y) ρgs(x, y) + λ = σ (1 + s y)s xx s x s y s xy + (1 + s x)s yy (1 + s x + s y) 3 (1), s(x, y) ± ¼½ Â; λ Lagrange»Â ( Ì p a, p s  p σ Ü È ÃÈ); σ «È Â; (x, y, xx, xy, yy) s(x, y) Ý Â, s x = s x, s xy = s x y, Ð Ù. (1), ¼ ± ¼, ± ² È Ð ÐÇ. ± ¼½ Â Æ Ê È : s(x, y)dxdy = () Ω, Ω º Ö.. p a Ý PAW, ± ¼ µæ p a Û ¹. Æ, p a «± ¼½  Ï. Ñ ÂÅ, ÉÜ r º r 1, É ¹ ³ Ü È, Ü È¾ È. Ü, ¼ Ñ Ç ¹ È, ¾ Ð È. ««Ê, ± ¼½Ñ ÍÄ Ï Ð º Ë, Æ Ô È, Ʊ ¼½. 1 Ó Ç Fig.1 Pressure acting on the bottom of the keyhole

Å Ö 7 Ç ±Ë ¾½. p a µ È, à Ú. þ É, p a ± ÆÚÝ,  p a (x, y) = [( µ I 1 π 1 r r1 ) ( )] 1 + C j exp 3x 3y σj A B 1 (x ) [( ) ( )] µ I 1 π 1 1 + C r r1 j exp 3x 3y σj A B (x < ) (3), µ Å ; I «Ü ; σ j Ü ³Â; A 1, A  B ÆÚÝ ³; C j p a Ý Â, C j ÒÜ Å Â¾  ÊÑ..3 σ Ý PAW Æ, ÖÌ Î σ»â. ± [1]  [15] σ ÖÌ» σ = σ m.3 1 (T T m ) RT 1.3 1 [ ( 1. 1 ln 1 + 3.1 1 3 )] a S exp RT (), σ m Ú T m ¼ «È Â, R»Â, a S ÚÉ S Â, T. 3 Ñ Ù mm Ê 3 «, Ñ «º ± ¾Â ÕÖÌ. º ¾»ĐÞ,  ± Þ, º ÖÔ± «Â Þ ÊÞ, º Ê»ĐÞ. ß Â º.,. PAW «º : (Ä Ar) Ê 3. L/min, Ê 1 mm/min, µ º 5 mm, Ü. mm, (Ä Ar) Ê 15 L/min, Å Ô Ê mm, ¼ mm. Ñ Ä «º ³Â 1. ÖÌ, Ä No.1  No., «Ü Ò, º Ô, Ç Á ; Ä No.3 No., «Ü, º Ï Ô, ÇÏÁ. Ø «Ü 13 A ¼ÖÌ ± Æ ÅÆ Đ¼½Â Ï. ½, Æ ± 3.97 mm, Ƽ ± ÁÔº,. º, ± µ z ³ (Ñ µ ³).73 mm, ± Ë µ z ³.975 mm, ±. mm. Ø 3 «Ü 135 A ¼ÖÌ ± Æ ÅÆ Đ¼½Â Ï. Ƽ, ± ÁÔº, Æ 1 PAW Ź ²Á Table 1 The PAW process parameters Sample Welding Arc voltage Penetration Keyhole current, A V condition condition No.1 15 19.5 PP PK No. 13 19. PP PK No.3 135.9 FP CK No. 1 1. FP CK No.5 15 1. FP CK No. 15 1.5 FP CK Note: PP partial penetration, - - FP full penetration, PK partial keyhole, CK complete keyhole Fusion line Keyhole boundary.975.73 3.97-1 -1 - - - - - -. -1-1 - - - - - (c) -1 - - - - - - - ÅÛ Ð 13 A»ÕË»¼ Fig. Predicted longitudinal cross section shape, transverse cross section shape and 3 D drawing shape (c) of keyhole with 13 A current Ô ¼ Á. º, ± µ z ³.9 mm, ± Ë µ z ³ 3.1 mm, ±.33 mm.

Ö ÓÄ : Î º»À À Æ 3 Ø Ñ «Ü ÖÌ ± Æ ¼½. Ð, ± Ï «Ü ڻРÚ. ÑÄ «Ü 5 A Ú, «Ü É 15 A - - Fusion line Keyhole boundary 3.1.9-1 -1 - - - - - -.33-1 -1 - - - - - (c) -1 - - - - - - - 3 ÅÛ Ð 135 A»ÕË»¼ Fig.3 Predicted longitudinal cross section shape, transverse cross section shape and 3 D drawing shape (c) of keyhole with 135 A current Ú 13 A ¼, ± Ü É 13 A Ú 135 A ¼, ÌÖ, ± - - 15 A 13 A 135 A 1 A 15 A 15 A Ú.51 mm; «± ¹ Ú.73 mm. -1-1 - - - - - - -1-1 - - - - - - - (c) -1-1 - - - - РŹ ²Á»¼ Fig. Predicted longitudinal cross section shape, transverse cross section shape and top surface shape (c) of keyhole with different welding parameters Æ Ð ÅÛ Đ Î Table Keyhole dimensions under different welding current Welding Keyhole Keyhole dimension at top surface, mm Keyhole dimension at back surface, mm current, A depth, mm Length Width Length Width 15.77.3.73 13 3.97 5.75.71 135 CK..3.. 1 CK.13.37 1.. 15 CK.13.3 1.. 15 CK.17.379 1..

Å Ö 7 ± Ï. Ó Ä ÍÇ ± Ø a  b ÖÌ 1 û, Ï Ï «Ü ڻРÚ, Í Í²± Ö Ú «Ü. Ò «Ü É 13 A Ú 135 A ¼, ± Ö Ú, É ( 3.97 mm) Áº Ê ( mm) ±. Á PAW, ± ¼ È ± ¼Ñ. ± Ö Þ È«Î, p a, p s, p σ  λ È. (1) ( ² È) ±, p a, p s Â È ÃÈ F P, F L  F λ. (1) ±, p σ ÃÈ F σ. ± ¼, F P + F L + F λ = F σ (5) 3 Ñ «Ü ± È Ã ÈÖÌ ( È» º Ê ). Ð, Ï «Ü Ú, λ ÈÂ, F L ±, F P. «Ü É 13 A 13 A ¼, F P É 11.5 1 3 N Ú 1.79 1 3 N, 1.9 1 3 N. ² F P, Ç ± Ö ¹ Ü. Æ, ÆÉ È ± Ñ ÛÆÄ Í., ± ² Ö (Ø 5), Ö A ± mm Ö, Ò s(x, y) mm; Ö B Ô ± ± mm Ö, Ò s(x, y) < mm. ÖÌ F P Ö A  B Ô ÆÄ. Ï «Ü Ú, ± Ú, ±, Ö A F P ÆÄ Ú (Ø ). «Ü 133 A ¼, ÆÄ 3.59%, Æ 3 Ð ÅÛ»³Ç Á Table 3 Values of various forces under different levels of welding current Current F λ F L F P F σ A 1 3 N 1 3 N 1 3 N 1 3 N 15.51.7 11.3 5. 13.3.3 11.5.193 13.5 1.1 1.79 7.9 135. 1.1 1.99 7.73 1.9 1.35 1.17 9.3 15.7 1. 15.3 1. 15.7 1.5 1.37 11. 5 ÆÕ A Á B Fig.5 Schematic of regions A and B with side view and Percentage, % 7 5 3 1 top view 13 133 13 135 Current, A ÆÕ A Á B Ó F P Ú Fig. Distribution of F P at region A and B «Ü 13 A ¼, ÆÄ 5.3%. Æ, ² Ü, «Ü ß± ÊÒ F P ± Ô, ± É Ñ º Áº Ê 5 ÐÆÆ A B ±. ± 1 º ³Â¼ PAW º Ã, à ÖÌ. «¼ Á ¼, º Ü Ñ À. Ý º Ñ ÀÜ, Á ± Ï. ± ÀÜ Ý Ò [3,13], «ÀÜ ¾ ¼± ÂÍ. Ø 7. «Ü 13 A ¼, ÀÜ, Ƽ, À¼, ± (Ø 7a). «Ü 135 A ¼, ÀÜ É Ð mv, À, ¼ Á º ± (Ø 7b). «Ü Í Ú¼, ÀÜ 1 mv, Ç ± ÏÇÏ. Ëà Ä, Úº Ëà Stemi DV/DR Æ ß Ù ß. Ø «Ü 13  135 A ¼ Å. ½, «Ü 13 A ¼ Ô, «¼ Á ; «Ü 135 A ¼º Ô, «¼ ÌÁ. Ò ÕÖÌ Ã.

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