Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 Themal Stess and Heat Tansfe Cefficient f Ceamics Stalk Having Ptubeance Dipping int Mlten Metal* Na-ki NOD**, Henda**, Wenbin LI**, Yasushi TSE**, Hiki OGUR** and Yusuke HIGSHI** ** Depatment f Mechanical Engineeing, yushu Institute f Technlgy Sensui-Ch 1-1 Tbata-u, itakyushu-shi, Fukuka, Japan E-mail: nda@mech.kyutech.ac.jp bstact Lw pessue die casting is defined as a net shape casting technlgy in which the mlten metal is injected at high speeds and pessue int a metallic die. The lw pessue die casting pcess plays an inceasingly imptant le in the fundy industy as a lw-cst and high-efficiency pecisin fming technique. In the lw pessue die casting pcess is that the pemanent die and filling systems ae placed ve the funace cntaining the mlten ally. The filling f the cavity is btained by fcing the mlten metal, by means f a pessuied gas, t ise int a ceamic tube having ptubeance, which cnnects the die t the funace. The ceamics tube, called stalk, has high tempeatue esistance and high csin esistance. Hweve, attentin shuld be paid t the themal stess when the stalk having ptubeance is dipped int the mlten aluminum. It is imptant t educe the isk f factue that may happen due t the themal stesses. In this pape, them-fluid analysis is pefmed t calculate suface heat tansfe cefficient. The finite element methd is applied t calculate the themal stesses when the stalk having ptubeance is dipped int the cucible with vaying dipping speeds. It is fund that the stalk with withut ptubeance shuld be dipped int the cucible slwly t educe the themal stess. ey wds: Themal Stess, Ceamics Stalk, Lw Pessue Die Casting Machine, Ptubeance, FEM 1. Intductin Geneally, stuctual engineeing ceamics ae widely used in all kinds f engineeing fields f thei advantages f high tempeatue esistance, csin esistance and abasin esistance. The ceamics mateial has been used f aut heat engine, gas tubine, stalk in the lw pessue die casting machine as shwn in Fig.1 (a), and ll in the galvaniing line (see Fig. 1 (b)). Lw pessue die casting machine (LPDC) is especially suitable f pducing axi-symmetic cmpnent such as cylinde head, pistn, and bake dum (1),(2). Ceamic tube called stalk has been used in the LPDC. Stalk has high tempeatue esistance and high csin esistance. Peviusly, the stalk was made f cast in which esulted in spiling the quality f the pduct due t the patial melting f mlten metal. Theefe, ceamics stalk was intduced t impve the life time f tube. Hweve, thee is still lw eliability f ceamics mainly due t lw factue tughness. *Received 16 Nv., 29 (N. e84-2) [DOI: 1.1299/jmmp.4.1198] Cpyight 21 by JSME 1198
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 Mving platen Die Ceamic Stalk stalk Metal fill 13 mm Φ14 mm Φ17 mm Steel plate Gas knives wiping 25mm 13 mm Pessuing gases mm R545 R5 15 mm Fill stalk Mlten luminum 75 Cucible 15 mm 1mm 15 mm Φ5 mm Φ17 mm a) Simple tube b) Stalk with ptubeance Fig. 1 (a) Schema f the lw pessue die casting (LPDC) machine (Nte that LPDC is smetimes called lw pessue casting in Japan) Mlten inc 48 Ceamic lls Zinc bath 54mm Fig. 1 (b) Zinc bath in the galvaniing line The ceamic stalk plays a citical functin in the LPDC because it eceives the mlten metal with high tempeatue fm the cucible. Hweve, attentin shuld be paid t the themal stess when the ceamics stalk is dipped int the mlten metal. It is imptant t educe the isk f factue because f lw factue tughness f ceamics. In this pape the finite vlume methd is applied t calculate suface heat tansfe cefficient. Then, the finite element methd is applied t calculate the themal stesses when the stalk having ptubeance is dipped int the cucible with vaying dipping speeds. Figue 1 (a) shws the mdel f ceamics stalk f simple mdel and stalk with ptubeance. 2. Effect f Heat Tansfe Cefficient n Themal Stess when Ceamic Dipping int Mlten Metal In this pape, we cnside a new themal stess pblem when ceamics cylinde is dipping int mlten metal. In this pblem, since the value f heat tansfe cefficient α is nt well knwn, fist, we will check the effect f α n the themal stess f ceamics. Hee, we cnside a simple tw-dimensinal (2D) cicula mdel in Fig. 3 (a) t investigate the effect f heat tansfe cefficient n the themal stess because Zukauskas (3) ppsed a 1199
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 13mm ρ 5 ρ 5 ρ5mm ρ5mm 13mm 2D cicle mdel 45mm 1mm 65mm D u 7mm 15mm 7mm 15mm 85mm 85mm (a) Simple tube (N. f element 195, N. f ndes2816) (b) Stalk with ptubeance (N. f element 14931, N. f ndes16278) Fig. 2 Finite element mesh f ceamics stalk (Nte that the ptubeance has the adius ρ 5mm ) Fig. 3 (a) 2D cicle mdel cnvenient fmula t estimate heat tansfe cefficient f 2D cicle (see Eq.1 in Sec. 3.2). In this pape, thee values f α ae assumed f bunday cnditins in the finite element methd analysis, fist α 6.348 Zu 1 W/m by Zukauskas fmula (4),(5), 7 2 secnd α max 1 1 W/m as a vey lage value f α, and thid α (2.886 FVM 1.214) 1 W/m given by applying finite vlume methd (see Fig.5 (c) in Sec. 3.2). Tempeatue f the mlten aluminum is assumed t be 75 C (123) (see Table 1 in Sec. 3.1), and the initial tempeatue f the 2D cicula mdel is assumed t be 2 C. Sialn is used f 2D cicula mdel (see Table 2 in Sec. 3.1) which has ttal f 51 elements and 548 ndes. The esults ae shwn in Figs. 3 (b) and 3 (c). Fm Fig. 3 (c), it is fund that the maximum stess max 192MPa at t 75s when α 6.348 Zu 1 W/m. F this case maximum stess is eached in a lng time and the value is smalle than the case f the vey lage α. Figue 4 (a) shws the tempeatue distibutin and maximum stess by Zukauskas fmula. The maximum stess 8 7 6 Maximum tempeatue at utside suface Tempeatue ( C) 5 4 3 2 α by Zukauskas α by FVM Vey Lagelage α α cente Maximum tempeatue at cente at utside suface 1 2 4 6 8 1 12 14 16 18 221 21 Time (s) Fig. 3 (b) Maximum tempeatue vs. time elatin f 2D mdel ( u 25mm/s ) 12
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 4 Maximum stess (MPa) 3 2 1 372MPa (vey lage α) 194MPa (FVM) 192MPa (Zukauskas) 2 4 6 8 1 12 14 15 18 2 21 Time (s) Fig. 3 (c) Maximum stess vs. time elatin f 2D mdel ( u 25mm/s ) appeas at the cente f cicle as shwn in Fig. 4 (a). Utiliing the lage value f α, it is fund that maximum stess max 372MPa 7 2 appeas at t.1s when α max 1 1 W/m. F this case the maximum stess is eached t be the lage value in a sht time. Figue 4 (b) shws the tempeatue distibutin and maximum stess f the lage α. s shwn in Fig. 4 (b), the maximum stess appeas nea suface. This is due t the lage tempeatue diffeence appeaing nea utside suface vey shtly. Figue 3 (c) shws maximum stess by finite vlume methd calculatin, max 194MPa at t.98s when α (2.886 FVM 1.214) 1 W/m (see Fig. 5 (c)). The time t each the maximum stess is shte than the Zukauskas fmula althugh the value is almst the same. Figue 4 (c) shws the tempeatue distibutin and maximum stess by finite vlume methd. s shwn in Fig. 4 (c), the maximum stess appeas nea C 716 65 59 526 462 399 335 272 28 145 81 Tempeatue MPa 192 168 143 119 95 71 47 23 -.7-24 -48 Stess max 192MPa Fig. 4 (a) Tempeatue and stess distibutin f 2D mdel by Zukauskas fmula ( u 25mm/s, t 75s ) 121
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 C 75 677 6 53 458 385 312 239 166 93 2 Tempeatue MPa 372 268 165 62-41 -144-247 -35-453 -557-66 Stess max 372MPa Fig. 4 (b) Tempeatue and stess distibutin f 2D mdel by vey lage α ( u 25mm/s, t.1s ) the suface at the bttm f cicle. This is due t the lage tempeatue diffeence appeaing nea the suface at the bttm f cicle. s shwn in Fig. 3 (c), the maximum stess due t the vey lage α is lage than that due t Zukauskas fmula and finite vlume methd. Fm the abve discussin, it is fund that just assuming a vey lage α des nt pvide cect themal stesses. Maximum stess f α using Zukauskas fmula and FVM is nealy the same, but the time f eaching maximum stess is diffeent. It may be theefe cncluded that the finite vlume methd is desiable f calculating themal stess f ceamics cectly. C 526 475 425 374 323 273 222 172 121 7 2 MPa 194 135 77 19-38 -97-155 -213-271 -329-387 2D cicle mdel D u max 194MPa Tempeatue Stess Fig. 4 (c) Tempeatue and stess distibutin f 2D mdel by finite vlume methd ( u 25mm/s, t.98s ) 122
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 Table 1 The Physical ppeties f mlten aluminum at 75 C (123) Physical ppety (dimensin) Themal cnductivity λ, W/m Rll diamete D, m inematics viscsity ν, mm 2 /s Isbaic specific heat C p, kj/kg Viscsity η, mpa s 3 5 Cnstants in Eq. (1) when Re 1 1 2 1 ( C1) 3 5 Cnstants in Eq. (1) when Re 1 1 2 1 ( n) 112.2.17.967 1.1 2.2.26.6 Table 2 Mechanical ppeties f ceamics Mechanical ppeties f ceamics (dimensin) Themal cnductivity, W/m Specific heat, J/kg Cefficient f linea expansin, 1/ Yung s mdulus, GPa(kgf/mm 2 ) Specific weight Pissn s ati 4 Pint bending stength, MPa (kgf/mm 2 ) Factue tughness, MN/m 3/2 Sialn 17 65 3. 1-6 294 (29979) 3.26.27 15 (17) 7.5 3. nalysis Methd f Suface Heat Tansfe Cefficient 3.1 nalysis Mdel and Mateial Ppeties In lw pessue die casting machine, the stalk is 17mm in diamete and 13 mm in length. s shwn in Fig. 1 the stalk has the ptubeance with the t adius ρ 5mm. The stalk is made f ceamic because f its high tempeatue esistance and high csin esistance. Tempeatue f the mlten aluminum is assumed t be 75 C, and the initial tempeatue f the ceamics stalk is assumed t be 2 C. Table 1 shws the physical Suface heat tansfe (W/m 2 ) 22 2 15 x 1 5 D x C C,D 1 2 3 4 5 6 x (mm) 65 Fig. 5 (a) Suface heat tansfe cefficient f 2D and axi-symmety mdel as a functin f in the mlten metal with the velcity u 25mm/s 123
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 Suface heat tansfe (W/m 2 ) 22 2 15 1 5 F E x x E F 1 2 3 4 5 6 x (mm) 65 Fig. 5 (b) Suface heat tansfe cefficient f simple tube and stalk with ptubeance mdels as a functin f in the mlten metal with the velcity u 25mm/s ppeties f mlten aluminum at 75 C (123) (5). Table 2 shws the mechanical ppeties f ceamics called Sialn (4) used f the stalk. xi-symmetic mdel will be used f simple tube with a ttal f 195 elements and 2816 ndes, and f stalk having ptubeance with a ttal f 14931 elements and 16278 ndes as shwn in Fig. 2. In this pape, lamina mdel (6),(7) is applied f finite vlume methd and 4-nde quadilateal elements ae emplyed f FEM analysis. 3.2 Suface Heat Tansfe Cefficient f Ceamics Stalk T calculate the themal stess, it is necessay t knw the suface heat tansfe cefficient α when the stalk dips int the mlten aluminum. In this pape, tw-dimensinal (2D) and axi-symmetic mdels ae analyed by using the finite vlume methd t calculate α when the stalk is dipped int the mlten metal. Figue 5(a) shws 12 Suface heat tansfe (W/m 2 ) 1 8 6 4 2 α max 1.214 1 W / m α min 2.886 1 W / m u -x (x,y) x O a α m 6.74 1 W / m -85-6 -4-2 2 4 6 85 x (mm) Fig. 5 (c) Suface heat tansfe as a functin f x f tw-dimensinal cylinde in the mlten metal with the velcity u 25mm/s 124
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 Table 3 suface heat tansfe cefficient α, W/m 2. Mdel 65mm 13mm Simple mdel unde vetical dipping (Mlten l T75 C) 85mm 7mm i 65mm 13mm Stalk having ptubeance mdel unde vetical dipping (Mlten l T75 C) 85mm 7mm i Cylinde mdel unde hintal dipping (Mlten l T75 C) 85mm 7mm i 65 (mm) 65 (mm) u 2mm/s F dipping step by step until eaching half tube: α 1.523 1 W/m Step 16 given α 1.523 1 W/m Step 8 Step 2 F dipping step by step until eaching half tube: α 1.523 1 W/m Step 16 α 1.523 1 W/m given Step 8 Step 2 F dipping step by step: α 1.523 1 W/m Step 6 i Step 2 α 1.523 1 W/m given u 25mm/s (1) t - 6s lng ute sufaces :-65mm 85mm α (2.534-19.15) 1 W/m lng inne sufaces i 7mm : - 65mm α (.831-19.516) 1 W/m F lwe end suface mm α 16.9 1 W/m α (.831-19.516) 1 W/m α (2.534-19.15) 1 W/m α 16.9 1 W/m (2) t 6s-6s F expsed suface until eaching half tube: α.831 1 W/m (1) t - 6s lng inne and ute sufaces i 7mm 85mm :-65mm α (.35-18.11) 1 W/m F lwe end suface mm α 15.91 1 W/m α (.35-15.281) 1 W/m α (2.527-18.11) 1 W/m α.25 1 W/m α.34 1 W/m α.25 1 W/m α 15.91 1 W/m α (2.24-3.64) 1 W/m α 1.13 1 W/m (2) t 6s-6s F expsed suface until eaching half tube: α.34 1 W/m (1) t - 6s lng ute sufaces 85mm α (2.886-1.214) 1 W/m t bth ends ±65mm α 2.886 1 W/m lng inne sufaces i 7mm α 2.886 1 W/m α 2.886 1 W/m α (2.886-1.214) 1 W/m (2) t > 6s F all expsed suface: α 2.886 1 W/m α 2.886 1 W/m α.831 1 W/m α.34 1 W/m the esults f α f the 2D and axi-symmetic mdels at u 25mm/s. F axi-symmetic mdel, the values f the suface heat tansfe cefficient α inne () and ute () f stalk ae diffeent as shwn in Fig. 5(a). It is cnfimed that when the diamete f the axi-symmetic mdel is infinity the value f α cincides with 2D esults. Figue 5(b) shws the suface heat tansfe cefficient α f stalk with ptubeance cmpaed with the simple tube at u 25mm/s. s shwn in Fig. 5(b) the values f α f inne (F) f stalk with ptubeance ae much smalle than thse f the simple tube (). The mlten metal cannt g int the stalk with ptubeance smthly and mst f the mlten metal has t detu the tube. Theefe, the ute α f stalk with ptubeance is als lwe than the ute α f the simple tube when < 2mm. Table 3 shws the values f suface heat tansfe cefficient α f simple tube and f stalk with ptubeance at u 2mm/s and u 25mm/s. In this sectin, the calculatin α f a tw-dimensinal cylinde using Zukauskas (5) is cmpaed with the finite vlume methd calculatin. Zukauskas (3) ppsed the fllwing equatin t estimate Nusselt numbe f a tw-dimensinal cylinde in the fluid with the velcity u..25 αm D n.37 P m 1 λ Pw Nu C Re P (1) u D Re, ν C P p η (2) λ 125
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 max, min (MPa) 4 3 2 1-1 -2 Maximum stess 296MPa max 1 max, min (MPa) 4 3 2 1-1 -2 max 296MPa (ptubeance) max 128MPa (simple) 1-3 -4 3 1 2 3 4 5 6 Time (s) -3-4 3 (ptubeance) 1 2 3 4 5 6 Time (s) Fig. 6 Maximum stesses vs. time elatin f stalk with ptubeance ( u 2mm/s, figues belw the abscissa shw the dipping level in the mlten aluminum) Hee, α m is the aveage suface heat tansfe cefficient, λ is themal cnductivity, D is the diamete f the cylinde, C 1 and n ae cnstants detemined by Reynlds numbe Re. ls, P is Pandtl numbe, and subscipt w dentes the ppety f tempeatue f cylinde wall. The velcity u can be calculated by the diamete f the tube divided by the time when the tube dips int the mlten aluminum, which is usually u 2 25mm/s. The values f isbaic specific heat C p, viscsity η, kinematics viscsity ν ae taken fm efeence (4), as shwn in Table 1. Substituting these int Eqs. (1) and (2), Nu m is calculated f the deteminatin f α m, which is, α 1.523 m 1 W/m (when u 2mm/s ). (3) α 6.348 m 1 W/m (when u 25mm/s ). (4) Figue 5 (c) shws the distibutin f suface heat tansfe cefficient as a functin f x f tw-dimensinal cylinde in the mlten metal with the velcity u 25mm/s. The esults f a 85mm in mlten aluminum ae btained by the applicatin f the finite vlume methd f tw-dimensinal cylinde mdel in the mlten metal with the velcity u 25mm/s. The esults in Fig. 5 (c) ae used in hintal tubes f calculatin f themal stess. In Fig.5 (c), the aveage value f α 6.74 m 1 W/m f a 85mm which is in ageement with Eq. (4). Fig. 7 Maximum stesses vs. time elatin f simple mdel ( u 2mm/s, figues belw the abscissa shw the dipping level in the mlten aluminum) max, min (MPa) 5 4 3 2 1 Maximum stess 1max 374MPa 1 max, min (MPa) 5 4 3 2 1 Maximum stess 1max 374MPa (ptubeance) 1 (ptubeance) Maximum stess 1max 246MPa (simple) 1 (simple) -1-1 -2-2 -3-3 3 (ptubeance) -4-4 x -5 3-5 3 (simple) x x -6-6 1 2 3 4 5 6 1 2 3 4 5 6 Time (s) Time (s) Fig. 8 Maximum stesses vs. time elatin Fig. 9 Maximum stesses vs. time elatin f stalk with ptubeance ( u 25mm/s ) f simple mdel ( u 25mm/s ) 126
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 4. Themal Stess f Simple Tube and Stalk with Ptubeance The simple tube and stalk having ptubeance with the length f 13mm as shwn in Fig.1 is cnsideed when half f the stalk is dipping int mlten aluminum at the speeds f u 2mm/s and u 25mm/s. It shuld be nted that u < 2mm/s is t slw and nt cnvenient and u > 25mm/s is t fast and nt safe. 4.1 Results f Dipping Slwly When u 2mm/s, a cnstant value α m 1.523 1 W/m is applied f dipping step by step alng the inne and ute sufaces ( i 7mm and 85mm ) until eaching half tube. Since it takes 328s f dipping cmpletely, sixteen types f patially dipping mdels ae cnsideed as shwn in Table 3, and the value α m 1.523 1 W/m is applied t the whle suface tuching mlten aluminum. The esults ae shwn in Figs. 6-7. These figues indicate the maximum tensile pinciple stess 1, maximum cmpessive pinciple stess 3, maximum stesses cmpnents,, and maximum shea stesses. Fm Fig. 7 it is seen that max cincides with 1 at t 2.5s f simple tube. Theefe, nly max will be discussed because it is almst equivalent t the maximum stesses 1. The stess max ( 1max ) has the peak value f 128MPa at t 2.5s f simple tube. On the the hand, the maximum stess 1max ( max ) has the peak value 1max 328MPa ( max 296MPa ) at t 41s f ceamics stalk with ptubeance as shwn in Fig. 6. Since the diectin f 1max is nt clea, Fig. 6 shws nly max because the value and diectin f 1max ae clse t the nes f max. F simple tube, the maximum stess max 128MPa appeas at t 2.5s and des nt decease while half f the stalk is dipping int mlten metal. Then, the stess deceases gadually afte half dipping is finished. Hweve, f stalk with ptubeance, the maximum stesses max 296MPa appeas nly at t 41s. fte t 41s the stess deceases and cincides with the esults f simple tube. Since sixteen types f patially dipping mdels ae utilied, fluctuatin f stesses appeas as shwn in Figs. 6 and 7. 4.2 Results f Dipping Fast In the pevius eseach (5) the Zukauskas fmula was used t calculate heat tansfe cefficient f dipping fast f themal stess analysis. In this pape the finite vlume methd is used t calculate heat tansfe cefficient f themal stess analysis. The esults will be cmpaed with the pevius eseach (5). Themal stess is cnsideed when the stalk in Fig. 1 dips int mlten aluminum fast at u 25mm/s. The suface heat tansfe is applied as fllws (see Table 3): 1. When t 6s, the values in Table 3 α (.831 19.516) 1 W/m is applied at the inne and ute sufaces f simple tube and α (.34 18.11) 1 W/m Detail f Detail f Detail f C Detail f D u2mm/s 95 C 17 C 246 C 322 C 397 C 472 C 548 C 623 C Tempeatue u2mm/s 39MPa 68MPa 98MPa max 128MPa 9.6MPa -19MPa -79MPa -18MPa -138MPa -49MPa -19MPa Fig. 1 Tempeatue and stess distibutin f simple mdel ( u 2mm/s, t 2.5s ) (ttm pats in the figue shw the dipping level in the mlten aluminum) u2mm/s C 99 C 179 C 259 C 339 C 419 C 498 C 578 C 658 C 738 C Tempeatue D u2mm/s 32MPa 85MPa 138MPa -2MPa 19MPa max 296MPa -125MPa -74MPa -2MPa -2MPa -74MPa -125MPa -49MPa Fig. 11 Tempeatue and stess distibutin f stalk with ptubeance ( u 2mm/s, t 41s) (ttm pats in the figue shw the dipping level in the mlten aluminum) 127
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 Detail f E Detail f F 177MPa 18MPa 9 C 39MPa E 16 C 299 C 369 C 439 C 59 C 579 C 719 C 649 C F -98MPa -167MPa -235MPa -373MPa max 246MPa f stalk with ptubeance. ls the maximum value, in Fig. 5 (b), α 16.9 1 W/m is applied at the lwe end suface ( mm ) f simple tube and α 15.9 1 W/m f stalk with ptubeance. 2. When t > 6s, the minimum value, in Fig. 5 (b) α.831 1 W/m is applied f the expsed suface until eaching half tube f simple tube and α.34 1 W/m f stalk with ptubeance. Figues 8 and 9 shw the maximum value f stesses 1,,,,. s shwn in Fig. 9, the maximum tensile stess 1 inceases in a sht time. fte taking a peak value 246MPa at t 1.1s f simple tube and 1max 374MPa ( max 363MPa ) at t 8.8s f stalk with ptubeance, it is deceasing. The maximum value f stalk with ptubeance 374MPa is lage than that f 246MPa f simple tube. F simple mdel, the maximum stess f dipping fast by finite vlume methd is 246MPa. Cmpaing this value with the maximum stess peviusly btained in Ref. (5) which is 219MPa. Thee is 1.9% in diffeence with the esults fm finite vlume methd. F heat tansfe cefficient, the maximum α is diffeent by 5%. 4.3 Cmpaisn between Dipping Slwly and Fast F simple tube, the maximum value 246MPa f dipping fast is lage than that f max 128MPa f dipping slwly. Similaly, f stalk with ptubeance, the Tempeatue Fig. 12 Tempeatue and stess distibutins f vetical tube ( u 25mm/s at time t 1.1s ), displacement 5 Detail f G Detail f H Detail f I 181 C 54 C 424 C 145MPa 1max 374MPa -236MPa -84MPa -236MPa 137MPa max 363MPa 62MPa -87MPa -162MPa -238MPa 585 C 262 C 342 C 424 C 342 C 54 C -16MPa 68MPa 145MPa 68MPa -16MPa 62MPa G 666 C 747 C 585 C H -77MPa -84MPa I -126MPa Tempeatue 1 Fig. 13 Tempeatue and stess distibutins f vetical tube ( u 2mm/s at time t 2.5s ), displacement 5 128
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 y 85mm 7mm 15mm x maximum stess 1max 374MPa f dipping fast is lage than that f 1max 328MPa f dipping slwly. Table 4 shws maximum stesses f stalk with ptubeance cmpaed with the esults f simple tube at the same time. s shwn in Table 4, the maximum value f stalk with ptubeance is 2.5 times lage than the value f simple tube at t 41s f u 2mm/s. On the the hand, f u 25mm/s the maximum value f stalk with ptubeance is 3.6 times lage than the value f simple tube at t 8.8s. The tempeatue and stess distibutins f simple tube and stalk with ptubeance ae indicated in Figs. 1-13. Figue 1 shws tempeatue and stess distibutins f at t 2.5s, whee the maximum stess max 128MPa appeas f the simple tube dipping slwly. F dipping slwly at u 2mm/s, the maximum stess appeas at the inne suface f the tube 7mm just abve the dipping level f mlten aluminum as shwn in Fig. 1. This is due t the bending mment caused by the themal expansin f the dipped ptin f the tube. Figue 12 shws tempeatue and stess distibutins at t 1.1s whee the maximum stess 246MPa appeas f the simple tube dipping fast. F the dipping fast at u 25mm/s, the maximum stess appeas n the inside f the thickness as shwn in Fig. 12. This is due t the lage tempeatue diffeence appeaing in the thickness diectin. It may be cncluded that simple tubes shuld be dipped slwly in de t educe the themal stesses. Figues 11 and 13 shw tempeatue and stess distibutins f f stalk with ptubeance dipping slwly and fast. Figue 11 shws tempeatue and stess distibutins f at t 41s, whee the maximum stess max 296MPa appeas f the stalk with Fig. 14 Finite element mesh f hintal tube (N. f elements45, N. f ndes55986) (MPa) 3 2 1-1 -2-3 -4-5 Maximum stess max 258MPa 1max max max max max min min min min 3max 2 4 6 8 1 Time (s) Fig. 15 Maximum stesses vs. time elatin f hintal tube ( u 2mm/s, figues belw the abscissa shw the dipping level in the mlten aluminum) (MPa) 3 2 1-1 -2-3 -4-5 -6 Maximum stess max 196MPa 1max maxmax max min max min min min 3max 1 2 3 4 5 Time (s) Fig. 16 Maximum stesses vs. time elatin f hintal tube ( u 25mm/s ) 129
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 ptubeance dipping slwly. F dipping slwly at u 2mm/s, the maximum stess appeas at the lwe t f the ptubeance ρ 5mm (see Fig. 11). This is due t the bending mment caused by the themal expansin f the dipped ptin f the tube. Figue 13 shws tempeatue and stess distibutins at t 8.8s whee the maximum stess max 363MPa appeas f stalk with ptubeance dipping fast. F the dipping fast at u 25mm/s, the maximum stess max appeas at uppe t f ptubeance ρ 5 as shwn in Fig. 13. This is due t the lage tempeatue diffeence appeaing in the utside the thickness and lwe pat f stalk. 5. Themal Stess f Hintal Tube Themal stess is cnsideed when the hintal tube in Fig. 14 dips int mlten aluminum at the speeds f u 2mm/s and u 25mm/s. Thee-dimensinal mdel will be used f hintal tube with a ttal f 45 elements and 55986 ndes as shwn in Fig. 14. 5.1 Results f Dipping Slwly When u 2mm/s, a cnstant value α m 1.523 1 W/m is applied f dipping step by step alng the inne and ute sufaces ( i 7mm, 85mm). Since it takes 21s f dipping cmpletely, six types f patially dipping mdels ae cnsideed as shwn in the Table 3, and the value α m 1.523 1 W/m is applied t the suface tuching mlten aluminum. Figue 15 shws maximum values f stesses 1,,,,. In Fig. 15, the maximum tensile stess 258MPa appeas at t 75s. 5.2 Results f Dipping Fast Similaly, t the vetical tube dipping fast, the Zukauskas fmula was peviusly used t calculate heat tansfe cefficient f hintal tube dipping fast (5). In this pape the finite vlume methd is used t calculate heat tansfe cefficient f themal stess analysis. Then, the esults will be cmpaed with the pevius eseach (5). Themal stess is cnsideed when the hintal tube in Fig. 14 dips int the mlten aluminum fast at u 25mm/s. Hee, the suface heat tansfe is applied in the fllwing way: 1. When t 6s, the values in Table 3 α (2.886 1.214) 1 W/m ae applied alng the ute suface ( 85mm ). ls the minimum value in Table 3 α 2.886 1 W/m is applied at the inne suface ( i 7mm ) and tube ends ± 65mm. 2. When t > 6s, the minimum value in Table 3 α 2.886 1 W/m is applied f all expsed sufaces. Figue 16 shws maximum values f stesses 1,,,,. s shwn in Fig. 16 the maximum stess inceases in a sht time, and has a peak value 196MPa at 228 C 124 C 2 C -25MPa -25MPa 437 C 645 C 333 C 541 C 645 C -25MPa 66MPa 158MPa -28MPa -117MPa max 258MPa 749 C -117MPa -25MPa Tempeatue 66MPa Fig. 17 (a) Tempeatue and stess distibutins f hintal tube at bth ends ± 65mm ( u 2mm/s at time t 75s ) 121
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 469 C 158 C 22 C -27MPa -115MPa 117MPa 4MPa 177-196MPa max 196MPa 656 C Tempeatue Fig. 17 (b) Tempeatue and stess distibutins f hintal tube nea the bth ends at 615mm ( u 25mm/s at time t 1.73s ) t 1.73s. F hintal tube, the maximum stess f dipping fast by the finite vlume methd is 196MPa. Cmpaing this value with the maximum stess peviusly btained in Ref. (5) which is 222MPa. Thee is 11% in diffeence with the esults fm the finite vlume methd. F heat tansfe cefficient, the maximum α is diffeent by 43%. 5.3 Cmpaisn between Dipping Slwly and Fast -48MPa Figue 17 (a) shws the tempeatue and stess distibutins f hintal tube at bth ends whee 258MPa appeas at t 75s f the tube dipping slwly. Figue 17 (b) shws tempeatue and stess distibutins nea bth ends, whee 196MPa appeas at t 1.73s f the tube dipping fast. F dipping slwly, as shwn in Fig. 18 (a) the maximum stess appeas at the inne suface f the tube ends ± 65mm. In this case the cicula css sectin becmes elliptical because f tempeatue diffeence between the dipped and uppe pats. In the wds, the maximum stess appeas due t asymmetic defmatin. F dipping fast as shwn in Fig. 18 (b), the tempeatue and stess distibutins ae simila t the nes f vetical tube dipping fast in Fig. 12. In the wds, f dipping fast, the defmatin is almst axi-symmetic. The lage stess appeas much me shtly than the case f u 2mm/s. Theefe hintal tubes shuld dip fast at u 25mm/s athe than slwly at u 2mm/s t educe the themal stess. y 8mm u y 749 676 63 53 457 385 312 239 166 9 C Tempeatue y u y 258 21 144 88 32-25 -81-138 -194-25 -37 MPa 258MPa Fig. 18 (a) Tempeatue and stess distibutins f hintal tube ( u 2mm/s at time t 75s ), displacement 3 1211
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 Detail f J y 22 C 282 C 345 C 47 C 1mm J 158 C Tempeatue 469 C 532 C 594 C 656 C Detail f y -37.4MPa -193MPa 4MPa 118MPa max 196MPa 177~196MPa -27MPa -348MPa -426MPa -48~-53MPa 35mm Fig. 18 (b) Tempeatue and stess distibutins f hintal tube ( u 25mm/s at time t 1.73s ), displacement 3 Table 4 Maximum stesses f stalk with ptubeance cmpaed with the esults f simple tube at the same time. Stalk with ptubeance Simple tube Hintal tube Mdel y x u2mm/s u25mm/s t t41s (maximum stess appeas) 1 328MPa () 296MPa () 162MPa () 167MPa () 15MPa () t t8.8s (maximum stess appeas) 1 374MPa () 363MPa () 181MPa () 116MPa () 98MPa () t t41s 1 12MPa () 12MPa () 11MPa () 4MPa () 28MPa () t t8.8s 1 11MPa () 11MPa () 97MPa () 7MPa(C) 18MPa () C t t2.5s (maximum stess appeas) 1 128MPa () 128MPa () 15MPa () 4MPa() 21MPa (C) t t1.1s (maximum stess appeas) 1 246MPa () 246MPa () 29MPa () 89MPa () 98MPa () C t t75s (maximum stess appeas) 1 258MPa 258MPa 21MPa 11MPa 116MPa t t1.73s (maximum stess appeas) 1 196MPa 196MPa 186MPa 112MPa 8MPa 5.4 Cmpaisn between the Results f Vetical and Hintal Tubes Table 4 shws the maximum values f tensile stesses f simple tube, stalk with ptubeance, and hintal tube. F bth simple tube and stalk with ptubeance, dipping slwly f ceamics stalk may be suitable f educing the themal stesses because dipping fast causes lage tempeatue diffeence in the thickness diectin, which esults in lage themal stesses. On the the hand, f hintal tube, dipping fast may educe the themal stess althugh in this case simila lage tempeatue diffeence appeas in the thickness diectin. Thse diffeent cnclusins may be explained in tems f defmatins f the tube. F simple tube and stalk with ptubeance, the defmatin is always axi-symmetic. Hweve, f hintal tube, dipping slwly causes lage asymmetic defmatin, which esults in the lagest at the inne suface f the end f the tube. On the the hand, f fast dipping f hintal tube, the defmatin is almst axi-symmetic. 6. Cnclusins In the ecent lw pessue die casting machine, the stalk is usually made f ceamics because f high tempeatue and csin esistances. Hweve, attentin shuld be paid t 1212
Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 the themal stesses when the stalk is dipped int the mlten aluminum. In this pape, the finite element methd in cnnectin with them-fluid analysis using the finite vlume methd f suface heat tansfe cefficient α was applied t calculate the themal stess when the stalk is installed in the cucible. The cnclusins ae given as fllwing. 1. Themal stess f 2D ceamic cicle was cnsideed. It was fund that accuate α distibutin is desiable f btaining accuate themal stess by applying the finite vlume methd (see Figs. 3 and 4). 2. Since the mlten metal cannt flw int the stalk with ptubeance vey much, the inne α f stalk with ptubeance is much lwe than the inne α f simple tube. ccuate α is shwn in Table 3 and Fig. 5 (b). 3. F bth simple tube and stalk with ptubeance, dipping slwly may be suitable f educing the themal stesses because dipping fast causes lage tempeatue diffeence in the thickness diectin, which esults in lage themal stesses. 4. F hintal tube, hweve, dipping fast may be suitable f educing the themal stess even thugh it causes lage tempeatue diffeence in the thickness diectin f the tube. 5. The diffeent cnclusins abut the vetical and hintal tubes may be explained in tems f defmatins f tube. F hintal tube, dipping slwly causes lage asymmetic defmatin, which esults in lage Refeences at the tube ends. (1) The t Z f Mateials luminum Casting Techniques-Sand Casting and Die Casting Pcesses. (Online), available fm <http://www.am.cm/details.asp? ticled1392>, (accessed 28-4-23). (2) nll, F., Uban, J., natt,., and tte, M., Gavity and Lw Pessue Die Casting f luminium llys: a Technical and Ecnmical enchmak, llumin E Leghe, (25). (3) Zukauskas,., Heat Tansfe fm Tubes in Css Flw, In: Hatnett JP, Ivine J TF, edits, dvances in Heat Tansfe, Vl.8, New Yk: cademic Pess, (1972), p. 131. (4) Nda, N.., Yamada, M., San, Y., Sugiyama, S., and bayashi, S., Themal Stess f ll-ceamics Rlls used in Mlten Metal t Pduce Stable High Quality Galvanied Steel Sheet, Engineeing Failue nalysis, Vl. 15, (28), pp. 261-274. (5) Nda, N.., Henda, Takase, Y., and Li, W., Themal Stess nalysis f Ceamics Stalk in the Lw Pessue Die Casting Machine, Junal f Slid Mechanics and Mateial Engineeing, Vl. 3, N.1 (29), pp. 19-11. (6) Li, H. S, and Mei, C., Themal Stess in SiC Element used in Heat Exchange, Junal Cent. Suth Univ. Technl., Vl. 12, N.6, (25), pp. 79-713. (7) l-zahanah, I. T., Yilbas,. S., and Hashmi, M. S. J., Cnjugate Heat Tansfe in Fully Develped Lamina Pipe Flw and Themally Induced Stesses, Cmpute Methds in pplied Mechanics and Engineeing, Vl. 19, (2), pp. 191-114. (8) Editial cmmittee f JSME, Data f heat tansfe, Tky: JSME, (1986), p.323 [in Japanese]. (9) enaga, I., Sialn Ceamics Pducts used in Mlten luminum, Skeiai (1991); 5:12-7 [in Japanese]. (1) Ngami, S., Lage Sialn Ceamics Pduct f Stuctual Use, Hitachi Metal Rept, Vl.15, (1999), pp.115-12 [in Japanese]. (11) Editial cmmittee f JSME, Data f heat tansfe, Tky: JSME; (1986), p.61 [in Japanese]. 1213