近畿大学次世代基盤技術研究所報告 Vol. 7（2016）89－94

SLM㐀ᙧ㐣⛬࡟࠾ࡅࡿ࣮ࣞࢨ↷ᑕ㒊㏆ഐࡢ⢊యᒙ⁐⼥จᅛࢆ⪃៖ࡋࡓ㐣Ώఏ⇕ᩘ್ゎᯒụᗉྖᩄᏕ*1㸪ிᴟ⚽ᶞ*2㸪⡿ཎ ∾Ꮚ*3㸪Ⲩᮌ ṇᾈ*4㸪୰ᮧ ࿴ஓ*4



Numerical Simulation of Transient Heat Conduction Analysis in Laser Illuminated Area
during SLM Process including Melting and Solidification of Powder Layer
Toshi-Taka IKESHOJI*1, Hideki KYOGOKU*2, Makiko YONEHARA*3,Masahiro ARAKI*4 and Kazuya NAKAMURA*4


The selective laser melting (SLM) is a kind of additive manufacturing processes, whichmelts the thin powder layer selectively and forms 3D object by compiling many layers. To obtain
the proper laser melting conditions for SLM process, the prediction of thermal field around thescanning laser spot is necessary. In this paper, a finite element method of transient heat
conduction analysis is proposed to predict the thermal field. It is based on the energy
conservation equation for enthalpy of bulk metal, powder metal and once-melt-and-solidified
powder metal. The method includes the phenomena of melting and solidification of powder metal.
The numerical simulation using this method is applied for Ni-based refractory alloy, Inconel-718,
and the results of the simulation is presented with temperature contours and dimensions of melt
pool.
Keywords: Additive Manufacturing, Inconel 718, Enthalpy of powder metals, Thermal
conductivity of powder metal ࡣࡌࡵ࡟㔠ᒓ୕ḟඖ✚ᒙ㐀ᙧ(Additive Manufacturing㸪AM)ࡣ㸪࣐ࢩࢽࣥࢢࢭࣥࢱ࣮➼ࢆ⏝࠸ࡓ㝖ཤຍᕤἲࡸ⢭ᐦ㗪㐀࡜ẚ㍑ࡋ࡚୕ḟඖⓗ࡛⮬⏤࡞ᙧ≧ࢆ๰⏕࡛ࡁࡿ࡜ᮇ
ᚅࡉࢀ࡚࠸ࡿ㸬AM ἲ࡟ࡣ࣮ࣞࢨ↷ᑕᆺሁ✚ἲ(LaserDeposition)㸪㟁Ꮚࣅ࣮࣒⁐⼥ἲ(Electron Beam Melting,EBM)࡞࡝ࡶ࠶ࡿࡀ㸪ᮏ◊✲࡛ࡣ࣮ࣞࢨ↷ᑕᘧࣃ࢘ࢲ࣮࣋ࢵࢻᆺ✚ᒙ㐀ᙧἲ(Selective Laser Melting㸪SLM)ࢆ
ᢅ࠺㸬SLM ࡣ㐀ᙧ≀ࡢ 3D ࣔࢹࣝࢆᩘ 10μm ཌࡉ࡟௬᝿ⓗ࡟ⷧࡃษ᩿ࡋ࡚ࢫࣛ࢖ࢫࣔࢹࣝࡘࡃࡾ㸪ࢫࣛ࢖ࢫࣔ
ࢹࣝ࡜ྠ➼࡞ᩘ 10μm ཌࡉ࡟ࡦ࠸ࡓ㔠ᒓ⢊యᒙࢆ࣮ࣞࢨ࡛㑅ᢥⓗ࡟⁐⼥จᅛࡉࡏࡿ㐣⛬ࢆ⧞ࡾ㏉ࡋ࡚⢊యᒙࢆ✚ᒙࡍࡿࡇ࡜࡟ࡼࡾ㸪㔠ᒓ 3D 㐀ᙧ≀ࢆᚓࡿ᪉ἲ࡛࠶ࡿ㸬
SLM ࡣ⢊యᒙཌࡉࡀⷧ࠸ࡇ࡜࡜㸪࣮ࣞࢨ࣮ࢫ࣏ࢵࢺ
ᚄࡀẚ㍑ⓗᑠࡉ࠸ࡓࡵ㸪௚ࡢ AM 㐣⛬࡜ẚ㍑ࡋ࡚ᙧ≧⢭ᗘࡀⰋ࠸࡜ࡉࢀ࡚࠸ࡿ㸬ࡋ࠿ࡋ㸪Ni ᇶྜ㔠ࡸࢫࢸࣥࣞࢫ㗰ࡢ㐀ᙧ࡛ࡣ㐀ᙧ≀ࡢኚᙧࡀၥ㢟࡜࡞ࡿሙྜࡀ࠶ࡿ㸬㐀ᙧ≀ࡢኚᙧࢆண ࡍࡿࡓࡵ࡟ࡣ࣮ࣞࢨ࣮ࢫ࣏ࢵࢺ࿘ࡾࡢ ᗘሙࢆ᫂ࡽ࠿࡟ࡍࡿࡇ࡜ࡀᚲせ࡛࠶ࡿ㸬
SLM 㐣⛬ࡢ࣮ࣞࢨ࣮ࢫ࣏ࢵࢺ࿘ࡾࡢ ᗘሙࢆ㐣Ώఏ⇕ゎᯒࡍࡿ◊✲ࡣࡇࢀࡲ࡛࡟ࡶ࡞ࡉࢀ࡚࠸ࡿ㸬
Matsumoto et.al. ࡣ 2 ḟඖ᭷㝈せ⣲ἲࢆ⏝࠸࡚ࣃ࢘ࢲཎ✏ཷ௜ 2016 ᖺ 5 ᭶ 7 ᪥*1 ㏆␥኱Ꮫ ḟୡ௦ᇶ┙ᢏ⾡◊✲ᡤ ෸ᩍᤵ㸦ࠛ739-2116 ᮾᗈᓥᕷ㧗ᒇ࠺ࡵࡢ㎶ 1 ␒㸧E-mail ikeshoji.tt@hiro.kindai.ac.jp*2 ㏆␥኱Ꮫ ᕤᏛ㒊 ࣟ࣎ࢸ࢕ࢡࢫᕤᏛ⛉ ᩍᤵ㸪ḟୡ௦ᇶ┙ᢏ⾡◊✲ᡤ ᩍᤵ㸦ࠛ739-2116 ᮾᗈᓥᕷ㧗ᒇ࠺ࡵࡢ㎶ 1 ␒㸧E-mail kyogoku@hiro.kindai.ac.jp*3 ㏆␥኱Ꮫ ḟୡ௦ᇶ┙ᢏ⾡◊✲ᡤ ◊✲ဨ㸦ࠛ739-2116 ᮾᗈᓥᕷ㧗ᒇ࠺ࡵࡢ㎶ 1 ␒㸧
*4 ᢏ⾡◊✲⤌ྜḟୡ௦㔠ᒓ 3D ✚ᒙᢏ⾡⥲ྜ㛤Ⓨᶵᵓ㸦TRAFAM㸧㏆␥኱Ꮫᗈᓥศᐊ ◊✲ဨ㸦ࠛ739-2116 ᮾᗈᓥᕷ㧗ᒇ࠺ࡵࡢ㎶ 1 ␒㸧㐃⤡ඛ㸸ụᗉྖᩄᏕ㸦◊✲௦⾲⪅㸧

－ 89 －࣮࣋ࢵࢻୖࢆ࣮ࣞࢨ㉮ᰝࡋࡓ≧ἣࢆ⢊య࠿ࡽᅛయ࡬ࡢኚ໬ࡣ⇕ఏᑟゎᯒ࡛┦ኚែࢆ⪃៖ࡋ࡚⾜ࡗࡓ(1)㸬3 ḟඖࡢ⇕ఏᑟゎᯒ࡜㐀ᙧ≀ࡢኚᙧࡢண ࡣ Zaeh & Brannerࡀ⾜ࡗࡓࡀ㸪⢊యࡢ≀ᛶ࡟ࡘ࠸࡚ࡣ⪃៖࡟ධࢀ࡚࠸࡞࠸
(2,3)㸬⢊యࡢ≀ᛶ್࡟ࡘ࠸࡚ࡣ Husseain, et.al ࡀ⢊య୰ࡢ✵Ꮝ⋡ࢆ߶ ࡛⇕ఏᑟ⋡ࢆ݇୮୭୵ୢୣ୰ ൌ ݇௕௨௟௞ ሺͳ െ ߶ሻ࡜᥎ᐃࡋ࡚࣮ࣞࢨ࣮ࢫ࣏ࢵࢺ࿘ࡾࡢ ᗘศᕸࢆ㐣Ώఏ⇕ゎᯒ࡛ᚓ࡚࠸ࡿ㸬ࡇࡢ⢊యࡢ⇕ఏᑟ⋡ࡣ Loeb ࡢࣔࢹࣝ࡜➼౯࡛࠶ࡿࡀ㸪᥎ᐃ್ࡀᐇ ್ࡼࡾࡶ 10 ಸ௨ୖ࡜࡞ࡿ㸬ྠᵝ࡞⢊యࣔࢹ࡛ࣝ⇕ఏᑟゎᯒ࡜ṧ␃ᛂຊゎᯒࢆ
Hodge, et.al.ࡀ⾜ࡗ࡚࠸ࡿ (4)㸬⢊యᒙࡢ⇕ఏᑟ⋡ࢆࡼࡾ⢭ᗘࡢ㧗࠸㏆ఝ࡛ゎᯒ࡟ྵࡵࡿࡇ࡜ࡀᚲせ࡛࠶ࡿ㸬⢊యᒙࡢ⇕ఏᑟ⋡࡟ࡘ࠸࡚ࡣከࡃࡢࣔࢹࣝࡀᥦ᱌ࡉࢀ࡚࠸ࡿ(5-10)㸬ከࡃࡢࣔࢹࣝࡣ⢊యࡢ⢏ᚄ‫ܦ‬୮ ࢆ୍ᐃ࡜ࡋ࡚᏶඲⌫ࡢ⢊యࡀ✵㝽⋡ Ԗ ࡛඘ሸࡉࢀ࡚࠸ࡿ࡜ࡋ㸪඘ሸࡢࡉࢀ᪉ࢆᗄఱᏛⓗ࡟⾲ࡋ㸪᥋ゐ⇕ఏ㐩࡜㍽ᑕ⇕ఏ㐩ࢆ⪃៖ࡋࡓࣔࢹࣝࢆసࡗ࡚࠸ࡿ㸬ᮏ◊✲࡛ࡣ⢊యࡢ⇕ఏᑟ⋡ࢆᐇ ್࡜ẚ㍑ⓗྜ⮴ࡍࡿ Kunii-Smith ࣔࢹࣝ(11,12)ࢆ⏝࠸㸪⁐⼥จᅛ⌧㇟ࡣ࢚ࣥࢱࣝࣆࢆ⏝࠸ࡓ࢚ࢿࣝࢠಖᏑ๎ࢆゎࡃࡇ࡜࡛⪃៖ࡋ㸪࠿ࡘ㸪⢊యࡢ⁐⼥จᅛ࡟ࡼࡿᐦᗘ㸪࢚ࣥࢱࣝࣆ㸪⇕ఏᑟ⋡ࡢ ᗘ౫Ꮡᛶࢆຍ࿡ࡍࡿ㸬 ゎᯒ᪉ἲSLM ࡢ㐀ᙧ᮲௳࡜ࡋ࡚ࡣ࣮ࣞࢨฟຊ(PW)㸪࣮ࣞࢨ࣮ࢫ࣏ࢵࢺᚄ(SD)㸪࣮ࣞࢨ㉮ᰝ㏿ᗘ(SS)㸪ࣁࢵࢳᖜ(dy)㸪
⢊యᒙཌࡉ(dz)ࡀ࠶ࡾ㸦ᅗ 1㸧
㸪SS㸪dy㸪dz ࢆ⤌ࡳྜࢃࡏࡓ࢚ࢿࣝࢠᐦᗘ  W/mm3 ࢆ┠Ᏻ࡜ࡍࡿ㸬ൌ ൈ  ൈ  ᮏゎᯒ࡛ࡣ Inconel 718 ࣂࣝࢡయࡢୖ࡟ཌࡉ dz = 50μm ࡢ⢊యᒙࡀ✚ᒙࡉࢀ࡚࠸ࡿ࡜ࡋࡓ㸬⢊యࡣ⢏ᚄ ‫ܦ‬୮ =40 μm ࡀ᭱␯඘ሸࡉࢀ㸪✵㝽⋡ࡣ Ԗ㸻0.476 ࡜ࡋࡓ㸬 㐀ᙧ᮲௳ࡣ PW = 292,W㸪SD = 0.1, mm㸪SS = 610,mm/s㸪dy = 0.15, mm ࡜ࡋ㸪࢚ࢿࣝࢠᐦᗘࡣ 63.8W/mm3 ࡜࡞ࡗࡓ㸬 ゎᯒ㡿ᇦࡣᖜ0.95㛗ࡉ5.5㧗ࡉ0.35 mm ࡢ┤᪉య࡜ࡋ㸪ᖜ᪉ྥ࡜㛗ࡉ᪉ྥࡢ➃࠿ࡽ 0.25mm ࡢ఩⨨ࢆཎⅬ࡟㸪㛗ࡉ᪉ྥ࡟ 5mm ࡢ⥺࡟ἢࡗ࡚࣮ࣞࢨࢆ㉮ᰝࡋ㸪ᖜ
᪉ྥ࡟ 0.15mm ࡎࡽࡋ࡚㸪ᢡࡾ㏉ࡋ 5mm ㉮ᰝࡋ㸪෌ࡧ㸪ࡎࡽࡋ࡚ᢡࡾ㏉ࡋࡓ࡜௬ᐃࡋࡓ㸦ᅗ 2㸧
㸬,QFRQHO ࡢ≀ᛶ್Inconel 718 ࡢ≀ᛶ್ࡣẚ㍑ⓗ᪂ࡋࡃ ᗘ౫Ꮡᛶࡶヲ⣽࡟ ᐃࡋࡓ Pottlacher, et.al. (13,14)ࡢ⤖ᯝࢆ⏝࠸ࡓ㸬ẚ࢚ࣥࢱࣝࣆ ݄ெ , J/kg ࡣ௨ୗࡢ࡜࠾ࡾ࡛࠶ࡿ㸬ᅗ 1. 㐀ᙧ᮲௳ࡢグྕ

ᅗ 2. ゎᯒ㡿ᇦ㸪༢఩ mm㸬െͳͲͶǡͻͺͻ ൅ ʹͺ͸ܶ ൅ ͲǤͳ͸ͷܶ ଶ‫ۓ‬ሺͶͲͲ ൏ ܶ ൏ ͳͲͲͲሻۖ
െ͵ͳͻǡʹͺͶ ൅ ͸ͷʹܶሺͳͲͲͲ ൏ ܶ ൏ ͳͷʹͺሻ݄ெ ሺܶሻ ൌ ଺ଷ‫۔‬െͶǤ͹ͷͻ͸ ൈ ͳͲ ൅ ͵ǤͷͷͺͲ ൈ ͳͲ ܶۖሺͳͷʹͺ ൏ ܶ ൏ ͳ͸ͳͲሻ‫ە‬െʹͺ͵ǡͺͷͶ ൅ ͹͹ͺܶሺͳ͸ͳͲ ൏ ܶ ൏ ʹͳͲͲሻᐦᗘ ߩ, kg/m3 ࡣͺʹͷ͸ǤͶʹ െ ͲǤʹͲͳͻܶ െ ͳǤ͵͹͹ͻ ൈ ͳͲିସ ܶ ଶ‫ۓ‬ሺͶͲͲ ൏ ܶ ൏ ͳͲͲͲሻۖͺ͵ͻʹ െ ͲǤͶ͵ͳܶሺͳͲͲͲ ൏ ܶ ൏ ͳͷʹͺሻߩ஺ ሺܶሻ ൌ ସ‫ͳ۔‬ǤͲͷͺ͹ ൈ ͳͲ െ ͳǤͺ͸͹ʹܶۖሺͳͷʹͺ ൏ ܶ ൏ ͳ͸ͳͲሻ‫ە‬ͺ͵͸͸ െ ͲǤͶͺͺܶሺͳ͸ͳͲ ൏ ܶ ൏ ʹͳͲͲሻẚ⇕ࡣ ܿ, J/(kg K) ࡣẚ࢚ࣥࢱࣝࣆࡢ ᗘᚤศࢆ࡜ࡗ࡚௨ୗࡢࡼ࠺࡟࡞ࡿ㸬ܿ஺ ሺܶሻ ൌ݄݀ெ݀ܶʹͺ͸ ൅ ͲǤ͵͵͹Ͳܶൌ  ቐ͸ͷʹ͹͹ͺሺͶͲͲ ൏ ܶ ൏ ͳͲͲͲሻ
ሺͳͲͲͲ ൏ ܶ ൏ ͳͷʹͺሻሺͳ͸ͳͲ ൏ ܶ ൏ ʹͳͲͲሻᐦᗘ࡜ẚ⇕࠿ࡽ༢఩య✚ᙜࡓࡾࡢ࢚ࣥࢱࣝࣆ, ݄௏ , J/m3,ࡣ௨ୗࡢࡼ࠺࡟⟬ฟ࡛ࡁࡿ㸬୘݄୚ǡସ଴଴ ሺܶሻ ൌ න ߩସ଴଴ ܿସ଴଴ ݀ܶସ଴଴ൌ െͳǤͳ͸ͲͲ ൈ ͳͲଽ ൅ ʹǤ͵͸ͳ͵ ൈ ͳͲ଺ ܶ ൅ ͳǤ͵͸ʹ͵ൈ ͳͲଷ ܶ ଶ െ ͵ǤͷͶ͵ͷ ൈ ͳͲିଶ ܶ ଷ െ ͳǤͳʹ͹ʹൈ ͳͲିହ ܶ ସ － 90 －୘݄୚ǡଵ଴଴଴ ሺܶሻ ൌ නߩଵ଴଴଴ ܿଵ଴଴଴ ݀ܶ ൅ ݄୴ǡସ଴଴ ሺͳͲͲͲሻଵ଴଴଴ൌ െͷǤ͵͵ͳͳ ൈ ͳͲଽ ൅ ͷǤͶ͹ͳ͸ ൈ ͳͲ଺ ܶ െ ͳǤͶͲͷͳൈ ͳͲଶ ܶ ଶ ൅ ݄୴ǡସ଴଴ ሺͳͲͲͲሻൌ െʹǤͺͳͶͳ ൈ ͳͲଽ ൅ ͷǤͶ͹ͳ͸ ൈ ͳͲ଺ ܶ െ ͳǤͶͲͷͳൈ ͳͲଶ ܶ ଶ ୘݄୚ǡ୤ ሺܶሻ ൌ නߩ୤ ܿ୤ ݀ܶ ൌ ݄୴ǡଵ଴଴଴ ሺͳͷʹͺሻଵହଶ଼ൌ െͶǤͻ͹ͻͻ ൈ ͳͲଵ଴ ൅ ͵Ǥ͹͸͸͸͹ ൈ ͳͲ଻ ܶെ ͵͵ʹͳǤ͹͸ܶ ଶ ൅݄୴ǡଵ଴଴଴ ሺͳͷʹͺሻൌ െͶǤͶͷͺͳ ൈ ͳͲଵ଴ ൅ ͵Ǥ͹͸͸͸͹ ൈ ͳͲ଻ ܶെ ͵͵ʹͳǤ͹͸ܶ ଶ୘݄୚ǡଵ଺ଵ଴ ሺܶሻ ൌ න

ᅗ 3. Inconel718 ࡢᐦᗘኚ໬ࡢ ᗘ౫Ꮡᛶߩଵ଴଴଴ ܿଵ଴଴଴ ݀ܶ ൅ ݄୚ǡ୤ ሺͳ͸ͳͲሻଵ଺ଵ଴ൌ െͻǤͻͺ͹ ൈ ͳͲଽ ൅ ͸ǤͷͲͺͺ ൈ ͳͲ଺ ܶ െ ͳǤͺͻͺ͵ൈ ͳͲଶ ܶ ଶ ൅ ݄୚ǡ୤ ሺͳ͸ͳͲሻൌ െʹǤͷ͵Ͷͷ ൈ ͳͲଽ ൅ ͸ǤͷͲͺͺ ൈ ͳͲ଺ ܶ െ ͳǤͺͻͺ͵ൈ ͳͲଶ ܶ ଶ ࡇࢀࢆ Inconel 718 ࣂࣝࢡయࡢ༢఩య✚ᙜࡓࡾࡢ࢚ࣥࢱ
ࣝࣆ࡜ࡋࡓ㸬݄஺ ሺܶሻ ൌ ݄୴ ሺܶሻ⇕ఏᑟ⋡ ɉ, W/(K m)ࡣ
ͳǤͳʹʹͶ ൅ ͲǤͲͳ͸ͷܶሺͳͲͲͲ ൏ ܶ ൏ ͳͷʹͺሻɉ୅ ሺܶሻ ൌ ൜ͶǤͺͻͺͷ ൅ ͲǤͲͳ͵͸ܶሺͳ͸ͲͲ ൏ ܶ ൏ ʹͳͲͲሻ
࡜ࡋࡓ㸬,QFRQHO ⢊యࡢ≀ᛶ್ Inconel 718 ⢊యࡢ≀ᛶ್ࡣ᥎ᐃ್ࢆ⏝࠸ࡓ㸬ᐦᗘɏ୆ ,kg/m3 ࡣ⢊యࡢ✵㝽⋡ Ԗ ࢆ⏝࠸࡚㸦ᅗ 3㸧
ߩ୆ ሺܶሻ ൌ ሺͳ െ Ԗሻߩ୅ ሺܶሻ ༢఩య✚ᙜࡓࡾࡢ࢚ࣥࢱࣝࣆ ݄୆ , J/m3 ࡣ㸦ᅗ 4㸧
݄୆ ሺܶሻ ൌ ሺͳ െ Ԗሻ݄୅ ሺܶሻ ⇕ఏᑟ⋡ࡣ Kunii-Smith ࣔࢹࣝ(12,13)ࢆ⏝࠸࡚᥎ᐃࡋࡓ㸬݄୰୴ ‫ܦ‬௣ߣ୆ ሺܶሻൌ Ԗ ቆͳ ൅ Ⱦቇ൅ߣ୥݇୥ᅗ 4. Inconel718 ࡢ༢఩య✚ᙜࡓࡾࡢ࢚ࣥࢱࣝࣆኚ໬ࡢ ᗘ౫ᏑᛶȾሺͳ െ Ԗሻߣ୥ͳ൅ߛ൬ ൰݄
‫ܦ‬ߣୱ
ͳ
୰ୱ ௣൅
߶ߣ୥

Ⱦ ࡣ⇕ὶࢀ᪉ྥࡢ⢊య⢏Ꮚ㛫㊥㞳࡜⢏ᚄࡢẚ࡛࠶ࡾ᭱␯඘ሸ࡞ࡢ࡛ Ⱦ = 1 ࡜ࡋࡓ㸬ߛ ࡣᅛయෆ⇕ఏᑟ࡟㛵ࡍࡿ⢏Ꮚᖹᆒཌࡉ࡜⢏Ꮚ┤ᚄࡢẚ࡛࠶ࡿࡀ㸪ߛ = 1 ࡜ࡋࡓ㸬߶ࡣ⢏Ꮚ࿘ᅖࡢẼయࡢ᭷ຠ⭷ཌࡉ࡜⢏Ꮚ┤ᚄࡢẚ࡛࠶ࡾ㸪ߢെͳ ଶ ଶቀቁ  ߠͳʹߢ߶ൌെʹ ݈݊ሺߢ െ ሺߢ െ ͳሻ  ߠሻ െ ߢ െ ͳ ሺͳ െ  ߠሻ ͵ߢߢࡇࡇ࡛㸪 ߠ = 0.839773,  ߠ = 0.542938 ࡜ࡋࡓ㸬ᅗ 5. Inconel718 ࡢ⇕ఏᑟ⋡ࡢ ᗘ౫Ꮡᛶ ݄୰୴ J/(m2 s K) ࡣ⢊య୰ࡢ✵㝽㸫✵㝽㛫ࡢ㍽ᑕఏ⇕ಀᩘ࡛࠶ࡾ㸪݄୰ୱ J/(m2 s K) ࡣᅛయ㠃㸫ᅛయ㠃㛫ࡢ㍽ᑕఏ⇕ಀᩘ࡛࠶ࡿ㸬－ 91 －݄୰୴ ൌྠᵝࡔ࠿ࡽ࡛࠶ࡿ㸬ࡋ࠿ࡋ㸪⇕ఏᑟ⋡ࡣ⁐⼥จᅛࡋ࡚✵㝽ࡀ࡞ࡃ࡞ࡗࡓࡓࡵࣂࣝࢡయ࡜ྠ➼࡛࠶ࡿ㸬#3 ࡣ⢊య࡛࠶ࡿ㸬ʹǤʹ͸ͻ͹͸ͻ͵ ൈ ͳͲିସ
ܶ ଷൈ൬
൰
ͳെȽ
Ԗ
ͳͲͲ
ͳ൅ʹሺͳ െ Ԗሻ ȽȽܶ ଷቁൈ൬
൰ʹെȽͳͲͲ 㞺ᅖẼẼయࡢ⇕ఏᑟ⋡ࡣHoshino, T, et.al.(15)ࡢᐇ㦂ᘧࢆ⏝࠸ࡓ㸬݄୰ୱ ൌ ʹǤʹ͸ͻ͹͸ͻ͵ ൈ ͳͲିସ ቀͻʹǤ͵ͻ൅ ͳǤ͸Ͷ͹ ൅ ͷǤʹʹͷ ൈ ͳͲିସ ܶ൰ܶᾮ┦⥺௨ୖࡢ ᗘᇦ࡛ࡢ Inconel 718 ⢊యࡢ⇕ఏᑟ⋡ࡣ Inconel 718 ࣂࣝࢡయࡢᾮయࡢ⇕ఏᑟ⋡࡜ྠࡌ࡜ࡋࡓ㸬⢊యࡶࣂࣝࢡయࡶ⁐⼥≧ែ࡛ࡣྠࡌᾮయࡔ࠿ࡽ࡛࠶ࡿ㸦ᅗ 5㸧㸬Kunii-Smith ࣔࢹࣝ࡟ࡼࡾ᥎ ࡋࡓ Inconel 718 ⢊యࡢ⇕ఏᑟ⋡ࡣ 1000 K ࡛⣙ 0.5 W/(m K)࡛㸪ࣂࣝࢡయࡢ
⇕ఏᑟ⋡⣙ 16 W/(m K)ࡢ 1/80 ⛬ᗘ࡜࡞ࡗࡓ㸦ᅗ 6㸧㸬⢊యࡢ⢏ᚄࡀ 4μm ࡜ 40μm ࡛ࡣ࡯ࡰྠ⛬ᗘ࡛࠶ࡿࡀ㸪
400μm ࡛ࡣ 1000K ࢆ㉸࠼ࡿ㧗 ᇦ࡛ 40μm ࡢሙྜ࡟ẚ࡭࡚ 5 % ⛬ᗘ኱ࡁࡃ࡞ࡗࡓ㸬✵㝽ࡀ኱ࡁࡃ࡞ࡗࡓࡓࡵ
㍽ᑕఏ⇕ࡢᙳ㡪ࡀ኱ࡁࡃ࡞ࡗࡓࡵ࡛࠶ࡿ㸬୍᪉㸪⢏ᚄࢆ
40μm ୍ᐃ࡜ࡋ࡚㍽ᑕ⋡ࢆ 0.1㹼0.50 ࡜ኚ໬ࡉࡏࡿ࡜㸪㍽ᑕ⋡ࡢቑຍ࡟క࠸⇕ఏᑟ⋡ࡶቑຍࡍࡿࡀ㸪㍽ᑕ⋡࡟ࡼࡿᕪ␗ࡣ኱ࡁࡃ࡞࠿ࡗࡓ㸦ᅗ 7㸧㸬⁐⼥จᅛࣔࢹࣝ
⢊యࡢ⁐⼥࡜จᅛࡣ᭷㝈せ⣲࡟๭ࡾᙜ࡚ࡓ≀ᛶ್ࢆ⠇Ⅼ ᗘ࡟ࡼࡾኚ᭦ࡍࡿࡇ࡜࡛ᮏゎᯒ࡟⤌ࡳ㎸ࢇ࡛࠸ࡿ㸬ࣂࣝࢡయࡢᐦᗘ㸪༢఩య✚ᙜࡓࡾࡢ࢚ࣥࢱࣝࣆ㸪⇕ఏᑟ⋡ࢆߩ஺ ሺܶሻ㸪݄஺ ሺܶሻ㸪ߣ୅ ሺܶሻ㸪⢊యࡢ≀ᛶ್ࢆߩ஻ ሺܶሻ㸪݄஻ ሺܶሻ㸪ɉ୥ ሺܶሻ ൌ ξܶ ൬െߣ୆ ሺܶሻ࡜ࡍࡿ㸬ゎᯒ࡟⏝࠸ࡿ≀ᛶ್㸦Mat. Prop㸧ࡣ 3 ✀㢮㸪#1~#3 ࡜ࡋࡓ㸦⾲ 1㸧㸬#1 ࡣ Inconel 718 ࣂࣝࢡయࢆ⾲ࡍ㸬#2 ࡣ Inconel 718 ⢊యࡀ㸪୍᪦㸪⁐⼥ࡋࡓᚋ࡟จᅛࡋࡓ≀㉁࡜ࡋࡓ㸬ࡇࡢ≀㉁ࡣ⢊య࡛ࡣ࡞ࡃ㸪ࣂࣝࢡయ࡛࠶ࡿࡀ᭷㝈せ⣲࡟༨ࡵࡿ≀㉁ࡢ㔞ࡀᑡ࡞ࡃ㸪ࣂࣝࢡయࡢͳ െ Ԗಸ࡛࠶ࡿ㸬ࡑࡢࡓࡵ㸪ᐦᗘ㸪༢఩య✚ᙜࡓࡾࡢ࢚ࣥࢱࣝࣆࡣ⢊యࡢ್ࢆ⏝࠸㸪⇕ఏᑟ⋡ࡣࣂࣝࢡయࡢ್ࢆ⏝࠸ࡓ㸬ࡇࢀࡣ Inconel 718 ⢊యࡀ᭷㝈せ⣲࡟༨ࡵࡿయ✚ࡀࣂࣝࢡయࡼࡾࡶᑠࡉ࠸ࡓࡵ㸪⁐⼥จᅛࡋࡓᚋ࡛ࡶ

ᅗ 6 . Kunii-Smith ࣔࢹࣝ࡟ࡼࡿ Inconel 718 ⢊యࡢ⇕ఏᑟࡢ⢏ᚄ࡟ࡼࡿኚ໬㸬ᅗ 7. Kunii-Smith ࣔࢹࣝ࡟ࡼࡿ Inconel 718 ⢊యࡢ⇕
ఏᑟࡢ㍽ᑕ⋡࡟ࡼࡿኚ໬㸦⢏ᚄ 40μm㸧
㸬⾲ 1㸬Inconel718 ࣂࣝࢡయ㸪⁐⼥จᅛ⢊య㸪⢊యࡢ≀ᛶ್㑅ᢥ
Mat.Prop.

ρ(T)

h(T)

λ(T)

#1AAABulk

#2

BB

A

Melted & Solidified
Powder#3BBBPowderᅗ 8. ࣮ࣞࢨ࣮ࢫ࣏ࢵࢺ࿘ࡾࡢ⁐⼥จᅛ࡟ࡼࡗ࡚ኚ᥮
ࡉࢀࡓ᭷㝈せ⣲㸦ୖ㸧࡜ ᗘศᕸ㸦ୗ㸧
㸬－ 92 － 1 ࡘࡢ᭷㝈せ⣲ࡀゎᯒึᮇ࡟⢊య࡜ࡍࡿ࡜㸪≀ᛶ್ࡣ#3 ࡛࠶ࡿ㸬㐣Ώఏ⇕ゎᯒࢆ㐍ࡵࡿ㏵୰࡛⇕ఏᑟ࡟ࡼࡾせ⣲⠇Ⅼࡢ ᗘࡀୖ᪼ࡋࡓ࡜ࡍࡿ㸬᭷㝈せ⣲࡟ྵࡲࢀࡿ඲
⠇Ⅼࡢ ᗘࡀᅛ┦⥺ࢆ㉸࠼ࡓ㝿࡟㸪≀ᛶ್ࢆ#2 ࡢ⁐⼥จᅛࡋࡓ⢊య࡟ኚ᭦ࡍࡿ㸬ᅗ 8 ࡟࣮ࣞࢨ㉮ᰝ㛤ጞᚋ 30 ᫬㛫ࢫࢸࢵࣉィ⟬ᚋࡢ᭷㝈せ⣲࡟๭ࡾᙜ࡚ࡽࢀࡓ≀ᛶ್࡜ᗘศᕸࢆ㸪ィ⟬㡿ᇦୖ㠃࡜᩿㠃࡛♧ࡍ㸬࣮ࣞࢨ㉮ᰝࡣᅗ୰ᕥ࠿ࡽྑ࡬㐍ࡴࡀ㸪ඛ㢌ࡢ࣮ࣞࢨ࣮ࢫ࣏ࢵࢺ࿘ࡾ࡛ࡣ᭷㝈せ⣲࡟ྵࡲࢀࡿ඲⠇Ⅼࡀᅛ┦⥺ ᗘ(1260°C)௨
ୖ࡟࡞ࡗ࡚࠸࡞࠸ࡓࡵ࡟ ᗘࡢࡳ㧗ࡃ࡞ࡾ㸪≀ᛶ್ࡀ#3
࠿ࡽ#2 ࡟஺᥮ࡉࢀ࡚࠸࡞࠸せ⣲ࡀほᐹࡉࢀࡓ㸬ቃ⏺᮲௳࠾ࡼࡧึᮇ᮲௳ ゎᯒ㡿ᇦࡢഃ㠃࡜ᗏ㠃ࡣ Inconel718 ࣂࣝࢡయࡀ㐃⥆ⓗ࡟⥆࠸࡚࠸ࡿ࡜ࡋ㸪⇕ఏᑟ⋡ 18 W/(m K)ࡢ⇕ὶฟቃ⏺᮲௳ࢆ㈇Ⲵࡋࡓ㸬ୖ㠃ࡣ❅⣲ࡢẼὶ࡟᫹ࡉࢀ࡚࠾ࡾ㸪⇕ఏ㐩⋡ 40 W/(m K)ࡢᒙὶ⇕ఏ㐩᮲௳ࢆ㈇Ⲵࡋࡓ㸬 ࣮ࣞࢨ↷ᑕ㒊ࡢ⾲㠃࡟ࡣ⇕ὶ᮰ࢆ㈇Ⲵࡋࡓ㸬࣮ࣞࢨࡢᙉᗘࡣ࢞࢘ࢩ࢔ࣥศᕸ࡟ᚑ࠺࡜ࡋࡓ㸬࣮ࣞࢨ↷ᑕ୰ᚰ࠿ࡽ‫ݎ‬, m ࡢ෇ᙧࡢෆഃࡢᙉᗘ ܲ,W ࡣ࣮ࣞࢨ࣮ࣃ࣮࣡ࢆܲ଴࡜ࡍࡿ࡜㸪మమܲሺሻ ൌ ܲ଴ ൫ͳ െ ିଶ୰ Τ୵ ൯‫ࢺࢵ࣏ࢫ࣮ࢨ࣮ࣞࡣ ݓ‬ᚄ࡛࠶ࡿ㸬ଵ ൏  ൏ ଶ ࡢ㍯≧ࡢ⠊ᅖࡢ⇕ὶ᮰ ‫ݍ‬, W/m2 ࡣమమమమܲ଴ ൫݁ ିଶ௥భ Τ௪ െ ݁ ିଶ௥మ Τ௪ ൯‫ ݍ‬ൌ ܲሺ‫ݎ‬ଶ ሻ െ ܲሺ‫ݎ‬ଵ ሻ ൌߨሺ‫ݎ‬ଶଶ െ ‫ݎ‬ଵଶ ሻ⇕ὶ᮰ࢆ㈇Ⲵࡍࡿ⠊ᅖࡣ ‫ ݎ‬൏ ʹ‫ࡓࡋ࡜ ݓ‬㸬 ゎᯒ㡿ᇦ୰ࡢࣂࣝࢡయ㸪⢊యࡢึᮇ ᗘࡣ 50°C ࡜ࡋࡓ㸬 ⤖ᯝ࡞ࡽࡧ࡟⪃ᐹ ᅗ 9 ࡟࣮ࣞࢨ㉮ᰝ࡟ࡼࡿゎᯒ㡿ᇦୖ㠃㸦࣮ࣞࢨ↷ᑕ㠃㸧ࡢ ᗘศᕸࡢኚ໬ࢆ♧ࡍ㸬࣮ࣞࢨ↷ᑕ㛤ጞ࠿ࡽ᭱ึࡢ㉮ᰝ(1st Path)ࡢ㏵୰(t = 6.15s)࡛ࡣ㸪࣮ࣞࢨ࣮ࢫ࣏ࢵࢺᚄ࡜ྠ⛬ᗘࡢᖜ࡛㸪࣮ࣞࢨ㉮ᰝ᪉ྥ࡟ࡘ࠸࡚ᑐ⛠࡞⁐⼥ụࡀᙧᡂࡉࢀࡓ㸬⁐⼥ụࡣ࡯ࡰ⣳㗽ᙧ࡛࠶ࡿࡀ㸪⁐⼥ᆅᚋ᪉࡛ࡣ㉮ᰝ᪉ྥ࡟┤⾜᪉ྥ࡟ᖹᆠ࡞ ᗘศᕸ࡜࡞ࡗࡓ㸬ᅗ 9. ゎᯒ㡿ᇦୖ㠃ࡢ ᗘศᕸ

ᅗ 10. ゎᯒ⤊஢᫬Ⅼ࡛ࡢ Inconel 718 ࣂࣝࢡయ(‫ݡ‬1)࡜⁐⼥จᅛࡋࡓ⢊య(‫ݡ‬2)㸬
－ 93 －ࡇࢀࡣ⁐⼥ụᚋ᪉࡛ࡣจᅛࡀ࠾ࡇࡾ㸪᭷㝈せ⣲ࡢ≀ᛶ್ࡀࣂࣝࢡయ࡜ྠࡌ⇕ఏᑟ⋡࡜࡞ࡗ࡚࠸ࡿࡓࡵ㸪⢊యࡢ㒊ศࡼࡾࡶఏ⇕࡟ࡼࡿ⇕ࡢᩓ㐓ࡀ኱ࡁ࠸ࡓࡵ࡜⪃࠼ࡽࢀࡿ㸬2 ␒┠ࡢ㉮ᰝ(2nd path)࡛ࡣ⁐⼥ụࡢഃ㠃ࡀᅗ୰ୖ᪉࡛ࡣ㉮ᰝ᪉ྥ࡟ᑐࡋ࡚⊃ࡃ࡞ࡾ㸪㠀ᑐ⛠࡞⣳㗽ᙧ࡜࡞ࡗࡓ㸬᭱ึࡢ㉮ᰝ࡟ࡼࡾ᪤࡟ᅗ୰ୖഃࡀจᅛࡋ࡚࠸ࡿࡓࡵ㸪ୗഃࡢ⢊యࡼࡾࡶ⇕ఏᑟ⋡ࡀ㧗ࡃ࡞ࡗ࡚࠸ࡿࡓࡵ࡜⪃࠼ࡽࢀࡿ㸬3 ␒┠ࡢ㉮ᰝ(3rd Path)࡛ࡣ⁐⼥ụࡢ㠀ᑐ⛠ࡣࡼࡾᙉㄪࡉࢀࡿࡼ࠺࡟࡞ࡗࡓ㸬⢊యࡢ⁐⼥จᅛࢆຍ࿡ࡋࡓゎᯒࣔࢹࣝ࡟ࡼࡾ⁐⼥ụࡀ㠀ᑐ⛠ᙧ≧࡟࡞ࡿࡇ࡜ࡀ᫂ࡽ࠿࡟࡞ࡗࡓ㸬 ⢊యᒙࡢึᮇ ᗘࡣ 50°C ࡜ࡉࢀࡓࡀ㸪ゎᯒᚋ㸪඲యⓗ࡟ 200°C ௨ୖ࡜࡞ࡗࡓ㸬ࡇࡢࡇ࡜࠿ࡽ㸪ᐇ㝿ࡢ㐀ᙧ࡟࡛ࡣ✚ᒙࢆ㔜ࡡࡿࡈ࡜࡟⢊యᒙࡀᙜึࡢ᝿ᐃ ᗘࡼࡾࡶ㧗࠸ ᗘ࡟ಖࡓࢀࡿࡇ࡜ࡀᠱᛕࡉࢀࡿ㸬 ゎᯒ⤊஢᫬Ⅼ࡛ࡢ⢊యࡀ๭ࡾᙜ࡚ࡽࢀࡓ᭷㝈せ⣲ࢆྲྀࡾ㝖࠸ࡓ Inconel 718 ࣂࣝࢡయ(#1)࡜⁐⼥จᅛࡋࡓ⢊య(#2)ࡀ๭ࡾᙜ࡚ࡽࢀࡓ᭷㝈せ⣲ࢆᅗ࡟♧ࡍ㸬Inconel 718
ࣂࣝࢡయࡢୖ࡟㸪ⓑ⥺࡛⦕ྲྀࡾࡉࢀࡓ⁐⼥จᅛࡋࡓ⢊యࡀ♧ࡉࢀ࡚࠸ࡿ㸬ⓑ⥺ࡀ஧㔜࡟࡞ࡗ࡚࠸ࡿ㒊ศࡣࡶ࡜ࡢ⢊యࡢཌࡉࢆ♧ࡋ࡚࠸ࡿ㸬࣮ࣞࢨ㉮ᰝࡢ➃Ⅼ࡛ࡣ࣮ࣞࢨ࣮ࢫ࣏ࢵࢺࡢ෇ᙧᙧ≧࡟ἢࡗࡓᙧ࡛⁐⼥จᅛࡋࡓᵝᏊࡀ⌧ࢀ࡚࠸ࡓ㸬ࡲࡓ㸪2 ␒┠ࡢ㉮ᰝ(2nd path)ࡢ➃Ⅼ࡛ࡣ๓ࡢ㉮ᰝ࡟ࡼࡿ⁐⼥จᅛ㒊࡜ࡢ㛫࡟ᮍ⁐⼥㒊ࡀṧࡉࢀ࡚࠸ࡓ㸬 ࡲ࡜ࡵ ⢊యࡢ⇕ఏᑟ⋡ࢆ Kunii-Smith ࣔࢹࣝࢆᑟධࡋ㸪࠿ࡘ㸪⢊యࡢ⁐⼥จᅛ࡟ࡼࡿᐦᗘ㸪࢚ࣥࢱࣝࣆ㸪⇕ఏᑟ⋡ࡢᗘ౫Ꮡᛶࢆຍ࿡ࡋࡓ㐣Ώఏ⇕ゎᯒࢆ⾜ࡗࡓ⤖ᯝ㸪
SLM 㐀ᙧ㐣⛬࡟࠾ࡅࡿ࣮ࣞࢨ↷ᑕ㒊㏆ഐࡢ ᗘศᕸࢆண ࡍࡿࡇ࡜ࡀ࡛ࡁࡓ㸬ཧ⪃ᩥ⊩(1) Matsumoto M, Shiomi M, Osakada K, Abe F,“Finite Element Analysis of Single Layer Forming onMetallic Powder Bed in Rapid Prototyping by
Selective Laser Processing”, International Journal ofMachine Tools and Manufacture,42,1(2002), 61-7.
(2) Zaeh M F, Branner G, “Investigations on ResidualStresses and Deformations in Selective LaserMelting”, Production Engineering, 4,1(2010), 35-45.
(3) Zaeh M F, Branner G, Krol T A, editors, A, “ThreeDimensional Fe-Model for the Investigation ofTransient Physical Effects in Selective Laser Melting”,
4th International Conference on Advanced Researchin Virtual and Physical Prototyping, VRAP 2009,October 6, 2009 - October 10, 2009; 2010; Leiria,
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