宇宙航空研究開発機構研究開発資料

JAXA Ｒesearch and Development Memorandum

ロケット用ターボポンプ玉軸受の冷却流れ圧力損失モデル

川崎 聡，  木村 俊哉，  内海 政春，  後藤 公成，  須田 一志

宇宙航空研究開発機構研究開発資料

2012年3月

JAXARM11013

宇 宙 航 空 研 究 開 発 機 構 研 究 開 発 資 料

013

11

Pressure Loss Model of the Coolant Flow through the Ball Bearing in Rocket Turbopump ^* Satoshi KAWASAKI

, Toshiya KIMURA

, Masaharu UCHIUMI

, Kosei GOTO

and Kazushi SUDA

Abstract

In this study, numerical investigation of coolant flow across the angular contact ball bearing in a rocket turbopump was performed to evaluate pressure loss of the bearing. The results show that the pressure loss tendencies against the bearing revolution speed were significantly different between the flow directions. It was mainly caused by the flow separation behind the ball and centrifugal force effect of swirl flow made by bearing revolution. Furthermore, we get a simplified pressure loss model of the bearing and it can approximately estimate the difference of the pressure losses between the flow directions.

Key Words: Bearing, Numerical Analysis, Pressure Loss, Rocket Turbopump

ߪߓ߼ߦ

㜞ㅦ࿁ォᯏ᪾ߩਥゲߦߪ㧘ࠕࠠࠪࡖ࡞⩄㊀ߣ࡜ࠫࠕ࡞

⩄㊀ࠍหᤨߦᡰᜬߢ߈ࠆࠕࡦࠡࡘ࡜₹ゲฃ߇᏷ᐢߊ૶↪

ߐࠇ㧘ਔᣇะߩࠕࠠࠪࡖ࡞⩄㊀ࠍฃߌࠆ႐วߪ㧘ⶄ೉ࠕ ࡦࠡࡘ࡜₹ゲฃ߿න೉ࠕࡦࠡࡘ࡜₹ゲฃࠍⶄᢙ㈩೉ߒߚ

⚵วߖᑼ߇ណ↪ߐࠇࠆޕ࿑1ߦࠕࡦࠡࡘ࡜₹ゲฃߩ᭴ㅧ

଀ࠍ␜ߔޕ

৻⥸↥ᬺᯏ᪾ߢߪ㧘޿ࠊࠁࠆẢṖᴤࠍ↪޿ߡゲฃߩẢ Ṗߣ಄ළࠍⴕߞߡ߅ࠅ㧘ẢṖ߅ࠃ߮಄ළߩᣇᴺ߿ᯏ᭴ߦ ߟ޿ߡߪ㧘⎇ⓥ㐿⊒߇ㅴࠎߢ޿ࠆ⁽¹⁾ޕ৻ᣇ㧘ᭂૐ᷷ⅣႺ ਅߢ↪޿ࠄࠇࠆࡠࠤ࠶࠻↪࠲࡯ࡏࡐࡦࡊߩゲฃߢߪ㧘৻

⥸⊛ߥẢṖᴤߩࠟ࡜ࠬォ⒖᷷ᐲએਅߦߥࠆߚ߼ẢṖᴤࠍ

૶↪ߔࠆߎߣߪ㔍ߒ޿ޕߘߎߢ㧘಄ළߦߪࡐࡦࡊߢ᣹࿶

ߒߚᭂૐ᷷ߩផㅴ೷ߩ৻ㇱࠍ೑↪ߒ㧘ẢṖߦߟ޿ߡߪ଻

ᜬེߦ฽ᶐߐߖߚ࠹ࡈࡠࡦߩ⒖⌕ߦࠃࠆ࿕૕ẢṖᣇᑼࠍ

↪޿ߡ޿ࠆޕ

ゲฃߩ಄ළ․ᕈߪߘߩᯏ⢻߿ኼ๮ߦᄢ߈ߥᓇ㗀ࠍ෸߷

ߔߚ߼㧘಄ළ․ᕈߩะ਄ߪ࠲࡯ࡏࡐࡦࡊߩା㗬ᕈะ਄ߦ ߅޿ߡ㊀ⷐߥ⺖㗴ߢ޽ࠆޕゲฃ಄ළߩࡔࠞ࠾࠭ࡓࠍ᣿ࠄ ߆ߦߔࠆߚ߼ߦߪ㧘ゲฃ๟ࠅߩࡈࡠ࡯ࡄ࠲࡯ࡦ߿ᵹേ․

ᕈߦߟ޿ߡ⹦⚦ߦᛠីߔࠆߎߣ߇ᔅⷐߢ޽ࠆޕ

Outer ring Cage Inner ring

Ball Double-guidedContact angle

Double guided type Matched mounting Fig. 1 Angular contact ball bearing

࿑ 2 ߦࡠࠤ࠶࠻↪࠲࡯ࡏࡐࡦࡊߩゲฃ಄ළᵹࠇߩ৻଀

ࠍ␜ߔޕࡐࡦࡊ⠀ᩮゞߦߡ᣹࿶ߐࠇߚᶧ૕ߩ৻ㇱࠍゲฃ

಄ළߦ↪޿ࠆߚ߼㧘಄ළᵹ㊂ߪࡐࡦࡊߩṳࠇᵹ㊂ߣߥࠅ ࡐࡦࡊല₸ߦᓇ㗀ࠍ෸߷ߔޕ߹ߚ㧘ࡠࠤ࠶࠻↪࠲࡯ࡏࡐ ࡦࡊߢߪࠕࠠࠪࡖ࡞⩄㊀ࠍ㊒ࠅวࠊߖࠆߚ߼ߦࡃ࡜ࡦࠬ

ࡇࠬ࠻ࡦᯏ᭴ࠍ↪޿ࠆߎߣ߇ᄙ޿⁽²⁾ޕ࿑2ߦ␜ߔゲฃ಄

ළᵹࠇ F2 ߪࠗࡦࡍ࡜಴ญ߆ࠄࠗࡦࡍ࡜⢛㕙㧔ࡃ࡜ࡦࠬ

ቶ㧕ࠍㅢࠅゲฃࠍᵹࠇࠆߚ߼㧘಄ළᵹ〝ߩ࿶ജ៊ᄬߪࠗ

ࡦࡍ࡜⢛㕙࿶ജಽᏓߦኻߒߡ߽ᓇ㗀ࠍਈ߃ࠆޕᓥߞߡ㧘 ࡠࠤ࠶࠻↪࠲࡯ࡏࡐࡦࡊ⸳⸘ߦ߅޿ߡࡐࡦࡊല₸߿ࡃ࡜

ࡦࠬࡇࠬ࠻ࡦߩࠬ࡜ࠬ࠻⩄㊀ࠍ♖ᐲ⦟ߊផቯߔࠆߚ߼ߦ

* ᐔᚑ24ᐕ1᦬6ᣣฃઃ(Received 6 January 2012)

*1 ቝቮャㅍࡒ࠶࡚ࠪࡦᧄㇱ ቝቮャㅍ♽ផㅴᛛⴚ⎇ⓥ㐿⊒࠮ࡦ࠲㧙

(Space Transportation Propulsion Research and Development Center, Space Transportation Mission Directorate)

*2 ᧲ᣣᧄࠬ࠲࡯ࡢ࡯ࠢࠬ㧔ᩣ㧕(East Japan Star Works co. ltd.)

*3 IHI IHI Corporation

2 宇宙航空研究開発機構研究開発資料　JAXA-RM-11-013

Inducer

1st Impeller

Turbine

Seal System F2

Shaft F1

2nd Impeller

Fig. 2 Typical coolant flow paths of bearings in rocket turbopump

ߪ㧘ゲฃߩ࿶ജ៊ᄬࠍᱜ⏕ߦᛠីߔࠆᔅⷐ߇޽ࠆޕ ࡠࠤ࠶࠻↪࠲࡯ࡏࡐࡦࡊߩゲฃ಄ළᵹࠇߦ㑐ߒߡߪ㧘

ࠬࡍ࡯ࠬࠪࡖ࠻࡞ࡔࠗࡦࠛࡦࠫࡦ㜞࿶ᶧ㉄࠲࡯ࡏࡐࡦࡊ ߩ₹ゲฃࠍኻ⽎ߦߒߚ CFD ⸃ᨆߣ࡜࡯ࠫࠬࠤ࡯࡞ࡕ࠺

࡞ߦࠃࠆⷐ⚛⹜㛎߇ႎ๔ߐࠇߡ޿ࠆ⁽³⁾ޕ⚵วߖᑼࠕࡦࠡ

ࡘ࡜₹ゲฃ㧞୘ߩ㑆߆ࠄࠫࠚ࠶࠻಄ළߔࠆᣇᴺߦߟ޿ߡ

⺞ߴࠄࠇߡ߅ࠅ㧘ౝベඨᓘߩჇടߦࠃࠆޟࡐࡦࡇࡦࠣޠ ߩലᨐࠍࠃࠅ㜞߼ࠆᣇᴺ߇ᬌ⸛ߐࠇߡ޿ࠆޕߚߛߒ㧘࿁

ォᢙߦߟ޿ߡߪ㧞ࠤ࡯ࠬߩ⹜㛎⚿ᨐᲧセ߇␜ߐࠇߡ޿ࠆ ߛߌߢ޽ࠅ㧘࿶ജ៊ᄬߦኻߔࠆ࿁ォᢙᓇ㗀ߩ⹦⚦߹ߢߪ ಽ߆ࠄߥ޿ޕ

ᧄ⎇ⓥߢߪ㧘⚵วߖᑼࠕࡦࠡࡘ࡜₹ゲฃࠍኻ⽎ߣߒߡ㧘 CFD ⸃ᨆߦࠃࠅゲฃ಄ළᵹࠇߣ࿁ォᢙߦࠃࠆ࿶ജ៊ᄬ ߩᄌൻࠍ⺞ߴߚޕߘߩ⚿ᨐ㧘࿁ォߦࠃࠆ࿶ജ៊ᄬߩᄌൻ ߪ㧘ゲฃߦኻߔࠆᵹࠇᣇะߦࠃࠅᄢ߈ߊ⇣ߥࠆߎߣ߇␜

ߐࠇߚޕߘߩᏅ⇣߇↢ߓࠆේ࿃ߦߟ޿ߡᬌ⸛ߒߡ◲ᤃࡕ

࠺࡞ᑼࠍ᭴▽ߒ㧘ゲฃ࿶ജ៊ᄬߩ࿁ォᢙᓇ㗀ߩផቯᣇᴺ ࠍ␜ߒߚޕ

ኻ⽎ࠕࡦࠡࡘ࡜₹ゲฃ

࿑1ߦ⸘▚ኻ⽎ߣߒߚᄖベਔ᩺ౝᑼߩࠕࡦࠡࡘ࡜₹ゲ ฃࠍ␜ߔޕᄖベ㧘ౝベ㧘₹㧘଻ᜬེ߆ࠄ᭴ᚑߐࠇ㧘₹ߪ 13୘㧘଻ᜬེߩࡐࠤ࠶࠻ߪᐔ౞ࡐࠤ࠶࠻ᒻ⁁㧔࿑3(a)㧕 ߢ޽ࠆޕౝベߪゲߣหㅦᐲߢ࿁ォߒ㧘ᄖベߪ࿕ቯߣߒߡ

޿ࠆޕ଻ᜬེߪ₹ߦ᛼ߐࠇࠆ⁁ᘒߢ₹ߩ౏ォㅦᐲߣหㅦ ᐲߢ࿁ォߒߡ޿ࠆߣ઒ቯߒߚޕ

₹ߩ⥄ォㅦᐲߣ౏ォㅦᐲߪ₹ߣ゠㆏㕙ߩ㑆ߦṖࠅ߇ή

޿ߣ઒ቯߔࠆߣᯏ᭴ቇ⊛ߦ᳞߼ࠆߎߣ߇ߢ߈ࠆ⁽⁴⁾ޕᧄゲ ฃߢߪ౏ォㅦᐲߪ0.42Z㧔Z㧦ゲߩ࿁ォㅦᐲ㧕ߢ޽ࠆޕ₹

ߩ⥄ォߪ㧘࿑1ߦ␜ߔធ⸅ⷺߣု⋥ߩゲ߹ࠊࠅߦ౏ォᣇ ะߣㅒะ߈ߦ࿁ォߒ㧘ᧄゲฃߢߪ⥄ォㅦᐲߪ2.8Zߢ޽ࠆޕ ߥ߅㧘ቯᩰ࿁ォᢙߪ40000rpmߣ⸳ቯߒߚޕ

⸘▚᧦ઙ

ᧄ⎇ⓥߢߪ㧘ゲฃන૕ߦኻߔࠆCFD⸘▚ߣ⚵วߖᑼゲ ฃ㧔⋥೉㧞୘㧕ߦ߅ߌࠆCFD⸘▚ࠍⴕߞߚޕ࿑3(a)ߦ⸘

▚㗔ၞࠍ㧘࿑3(b)ߦゲฃන૕ߩ⸘▚ᩰሶࠍ㧘࿑3(c)ߦ⚵

วߖᑼߩ⸘▚ᩰሶࠍ␜ߔޕ

ゲฃන૕ߦ߅޿ߡ㧘࿑3(b)ߦ␜ߔࠃ߁ߦౝベߣᄖベߩ

⁜޿஥߆ࠄゲฃߦᵹࠇㄟ߻ᣇะࠍ㗅ᣇะ㧘ౝベߣᄖベߩ ᐢ޿஥߆ࠄᵹࠇㄟ߻ᣇะࠍㅒᣇะߣ๭߱ߎߣߦߔࠆޕ⚵

วߖᑼߩ႐วߪ㧘਄ᵹ஥ゲฃ߇න૕ߩ㗅ᣇะ㧘ਅᵹ஥ゲ ฃ߇න૕ߩㅒᣇะߦ⋧ᒰߔࠆޕ

CFD ⸃ ᨆ ߪ 㧘 Ꮢ ⽼ ߩ ᵹ ૕ ⸃ ᨆ ࠰ ࡞ ࡃ ࡯STARCCM+

㧔V5.02㧕ࠍ↪޿㧘⸘▚ߪቯᏱ⸃ᨆߢ₹߅ࠃ߮଻ᜬེߩ࿁

ォ♽ߢⴕߞߚޕᓥߞߡ㧘₹߅ࠃ߮଻ᜬེߦኻߔࠆ⋧ኻ⊛

ߥ࿁ォㅦᐲࠍౝベო㕙ߣᄖベო㕙ߦਈ߃ߡ޿ࠆޕ߹ߚ㧘

₹ߩ⥄ォ߽⠨ᘦߒߡ⥄ォㅦᐲࠍ₹⴫㕙ߦႺ⇇᧦ઙߣߒߡ ਈ߃ߚޕ

⸘▚㗔ၞߪ₹㧝୘ಽࠍขࠅ಴ߒ㧘஥㕙ߦߪ๟ᦼႺ⇇᧦

ઙࠍਈ߃ߡ޿ࠆޕ਄ᵹႺ⇇ߪ৻ቯߩᵹ㊂᧦ઙ㧔ో๟ߢ9.1 L/s㧕㧘ਅᵹႺ⇇ߦߪ࿶ജႺ⇇ࠍਈ߃ߡ޿ࠆޕੂᵹࡕ࠺࡞

ߪ㧘Realizable k-H㧔two layer㧕ࡕ࠺࡞ࠍ↪޿ߚޕ⸃ᨆᩰ

ሶߪ㧘ࡋࠠࠨ㧘ࡊ࡝࠭ࡓ㧘࠹࠻࡜ߩࡂࠗࡉ࡝࠶࠼㕖᭴ㅧ

ᩰሶߢ㧘ᩰሶଐሽᕈࠍ⺞ߴࠆߚ߼ゲฃන૕ߩࡕ࠺࡞ߦ߅

޿ߡ㧘⚂20ਁ࠮࡞߆ࠄ⚂300ਁ࠮࡞ߩ㑆ߢᲧセߒߚ⚿ᨐ ߆ࠄ㧘⚂150ਁ࠮࡞ߩࡕ࠺࡞ࠍណ↪ߒߚޕ⚵วߖᑼゲฃ ߩࡕ࠺࡞ߢߪ⚂300ਁ࠮࡞ߣߥࠆޕߥ߅㧘₹ߣౝベ߅ࠃ

߮ᄖベߩ㑆ߦߪធ⸅ὐ㧔ᒢᕈ૕ߣߒߡ⠨߃ߚ႐วߪធ⸅

㕙㧕߇ሽ࿷ߔࠆ߇㧘ᧄ⸘▚ߢߪࠊߕ߆ߥ㓗㑆ࠍ⸳ߌߡᩰ

ሶࠍ૞ᚑߒߚޕ

ᵹ૕ߪ㕖࿶❗᧦ઙߩᶧ૕᳓⚛ߣߒ㧘ቯᏱ⸘▚ࠍታᣉߒ ߚޕߥ߅㧘ᧄ⸘▚ߢߪゲฃߩ⊒ᾲ╬ߩᾲᓇ㗀߿ᶧ૕ߩ⋧

ᄌൻߪ⠨ᘦߒߡ޿ߥ޿ޕ

Inducer

1st Impeller

Turbine

Seal System F2

Shaft F1

2nd Impeller

Fig. 2 Typical coolant flow paths of bearings in rocket turbopump

ߪ㧘ゲฃߩ࿶ജ៊ᄬࠍᱜ⏕ߦᛠីߔࠆᔅⷐ߇޽ࠆޕ ࡠࠤ࠶࠻↪࠲࡯ࡏࡐࡦࡊߩゲฃ಄ළᵹࠇߦ㑐ߒߡߪ㧘

ࠬࡍ࡯ࠬࠪࡖ࠻࡞ࡔࠗࡦࠛࡦࠫࡦ㜞࿶ᶧ㉄࠲࡯ࡏࡐࡦࡊ ߩ₹ゲฃࠍኻ⽎ߦߒߚ CFD ⸃ᨆߣ࡜࡯ࠫࠬࠤ࡯࡞ࡕ࠺

࡞ߦࠃࠆⷐ⚛⹜㛎߇ႎ๔ߐࠇߡ޿ࠆ⁽³⁾ޕ⚵วߖᑼࠕࡦࠡ

ࡘ࡜₹ゲฃ㧞୘ߩ㑆߆ࠄࠫࠚ࠶࠻಄ළߔࠆᣇᴺߦߟ޿ߡ

⺞ߴࠄࠇߡ߅ࠅ㧘ౝベඨᓘߩჇടߦࠃࠆޟࡐࡦࡇࡦࠣޠ ߩലᨐࠍࠃࠅ㜞߼ࠆᣇᴺ߇ᬌ⸛ߐࠇߡ޿ࠆޕߚߛߒ㧘࿁

ォᢙߦߟ޿ߡߪ㧞ࠤ࡯ࠬߩ⹜㛎⚿ᨐᲧセ߇␜ߐࠇߡ޿ࠆ ߛߌߢ޽ࠅ㧘࿶ജ៊ᄬߦኻߔࠆ࿁ォᢙᓇ㗀ߩ⹦⚦߹ߢߪ ಽ߆ࠄߥ޿ޕ

ᧄ⎇ⓥߢߪ㧘⚵วߖᑼࠕࡦࠡࡘ࡜₹ゲฃࠍኻ⽎ߣߒߡ㧘 CFD ⸃ᨆߦࠃࠅゲฃ಄ළᵹࠇߣ࿁ォᢙߦࠃࠆ࿶ജ៊ᄬ ߩᄌൻࠍ⺞ߴߚޕߘߩ⚿ᨐ㧘࿁ォߦࠃࠆ࿶ജ៊ᄬߩᄌൻ ߪ㧘ゲฃߦኻߔࠆᵹࠇᣇะߦࠃࠅᄢ߈ߊ⇣ߥࠆߎߣ߇␜

ߐࠇߚޕߘߩᏅ⇣߇↢ߓࠆේ࿃ߦߟ޿ߡᬌ⸛ߒߡ◲ᤃࡕ

࠺࡞ᑼࠍ᭴▽ߒ㧘ゲฃ࿶ജ៊ᄬߩ࿁ォᢙᓇ㗀ߩផቯᣇᴺ ࠍ␜ߒߚޕ

ኻ⽎ࠕࡦࠡࡘ࡜₹ゲฃ

࿑1ߦ⸘▚ኻ⽎ߣߒߚᄖベਔ᩺ౝᑼߩࠕࡦࠡࡘ࡜₹ゲ ฃࠍ␜ߔޕᄖベ㧘ౝベ㧘₹㧘଻ᜬེ߆ࠄ᭴ᚑߐࠇ㧘₹ߪ 13୘㧘଻ᜬེߩࡐࠤ࠶࠻ߪᐔ౞ࡐࠤ࠶࠻ᒻ⁁㧔࿑3(a)㧕 ߢ޽ࠆޕౝベߪゲߣหㅦᐲߢ࿁ォߒ㧘ᄖベߪ࿕ቯߣߒߡ

޿ࠆޕ଻ᜬེߪ₹ߦ᛼ߐࠇࠆ⁁ᘒߢ₹ߩ౏ォㅦᐲߣหㅦ ᐲߢ࿁ォߒߡ޿ࠆߣ઒ቯߒߚޕ

₹ߩ⥄ォㅦᐲߣ౏ォㅦᐲߪ₹ߣ゠㆏㕙ߩ㑆ߦṖࠅ߇ή

޿ߣ઒ቯߔࠆߣᯏ᭴ቇ⊛ߦ᳞߼ࠆߎߣ߇ߢ߈ࠆ⁽⁴⁾ޕᧄゲ ฃߢߪ౏ォㅦᐲߪ0.42Z㧔Z㧦ゲߩ࿁ォㅦᐲ㧕ߢ޽ࠆޕ₹

ߩ⥄ォߪ㧘࿑1ߦ␜ߔធ⸅ⷺߣု⋥ߩゲ߹ࠊࠅߦ౏ォᣇ ะߣㅒะ߈ߦ࿁ォߒ㧘ᧄゲฃߢߪ⥄ォㅦᐲߪ2.8Zߢ޽ࠆޕ ߥ߅㧘ቯᩰ࿁ォᢙߪ40000rpmߣ⸳ቯߒߚޕ

⸘▚᧦ઙ

ᧄ⎇ⓥߢߪ㧘ゲฃන૕ߦኻߔࠆCFD⸘▚ߣ⚵วߖᑼゲ ฃ㧔⋥೉㧞୘㧕ߦ߅ߌࠆCFD⸘▚ࠍⴕߞߚޕ࿑3(a)ߦ⸘

▚㗔ၞࠍ㧘࿑3(b)ߦゲฃන૕ߩ⸘▚ᩰሶࠍ㧘࿑3(c)ߦ⚵

วߖᑼߩ⸘▚ᩰሶࠍ␜ߔޕ

ゲฃන૕ߦ߅޿ߡ㧘࿑3(b)ߦ␜ߔࠃ߁ߦౝベߣᄖベߩ

⁜޿஥߆ࠄゲฃߦᵹࠇㄟ߻ᣇะࠍ㗅ᣇะ㧘ౝベߣᄖベߩ ᐢ޿஥߆ࠄᵹࠇㄟ߻ᣇะࠍㅒᣇะߣ๭߱ߎߣߦߔࠆޕ⚵

วߖᑼߩ႐วߪ㧘਄ᵹ஥ゲฃ߇න૕ߩ㗅ᣇะ㧘ਅᵹ஥ゲ ฃ߇න૕ߩㅒᣇะߦ⋧ᒰߔࠆޕ

CFD ⸃ ᨆ ߪ 㧘 Ꮢ ⽼ ߩ ᵹ ૕ ⸃ ᨆ ࠰ ࡞ ࡃ ࡯STARCCM+

㧔V5.02㧕ࠍ↪޿㧘⸘▚ߪቯᏱ⸃ᨆߢ₹߅ࠃ߮଻ᜬེߩ࿁

ォ♽ߢⴕߞߚޕᓥߞߡ㧘₹߅ࠃ߮଻ᜬེߦኻߔࠆ⋧ኻ⊛

ߥ࿁ォㅦᐲࠍౝベო㕙ߣᄖベო㕙ߦਈ߃ߡ޿ࠆޕ߹ߚ㧘

₹ߩ⥄ォ߽⠨ᘦߒߡ⥄ォㅦᐲࠍ₹⴫㕙ߦႺ⇇᧦ઙߣߒߡ ਈ߃ߚޕ

⸘▚㗔ၞߪ₹㧝୘ಽࠍขࠅ಴ߒ㧘஥㕙ߦߪ๟ᦼႺ⇇᧦

ઙࠍਈ߃ߡ޿ࠆޕ਄ᵹႺ⇇ߪ৻ቯߩᵹ㊂᧦ઙ㧔ో๟ߢ9.1 L/s㧕㧘ਅᵹႺ⇇ߦߪ࿶ജႺ⇇ࠍਈ߃ߡ޿ࠆޕੂᵹࡕ࠺࡞

ߪ㧘Realizable k-H㧔two layer㧕ࡕ࠺࡞ࠍ↪޿ߚޕ⸃ᨆᩰ

ሶߪ㧘ࡋࠠࠨ㧘ࡊ࡝࠭ࡓ㧘࠹࠻࡜ߩࡂࠗࡉ࡝࠶࠼㕖᭴ㅧ

ᩰሶߢ㧘ᩰሶଐሽᕈࠍ⺞ߴࠆߚ߼ゲฃන૕ߩࡕ࠺࡞ߦ߅

޿ߡ㧘⚂20ਁ࠮࡞߆ࠄ⚂300ਁ࠮࡞ߩ㑆ߢᲧセߒߚ⚿ᨐ ߆ࠄ㧘⚂150ਁ࠮࡞ߩࡕ࠺࡞ࠍណ↪ߒߚޕ⚵วߖᑼゲฃ ߩࡕ࠺࡞ߢߪ⚂300ਁ࠮࡞ߣߥࠆޕߥ߅㧘₹ߣౝベ߅ࠃ

߮ᄖベߩ㑆ߦߪធ⸅ὐ㧔ᒢᕈ૕ߣߒߡ⠨߃ߚ႐วߪធ⸅

㕙㧕߇ሽ࿷ߔࠆ߇㧘ᧄ⸘▚ߢߪࠊߕ߆ߥ㓗㑆ࠍ⸳ߌߡᩰ

ሶࠍ૞ᚑߒߚޕ

ᵹ૕ߪ㕖࿶❗᧦ઙߩᶧ૕᳓⚛ߣߒ㧘ቯᏱ⸘▚ࠍታᣉߒ ߚޕߥ߅㧘ᧄ⸘▚ߢߪゲฃߩ⊒ᾲ╬ߩᾲᓇ㗀߿ᶧ૕ߩ⋧

ᄌൻߪ⠨ᘦߒߡ޿ߥ޿ޕ

Revolution direction of inner ring, ball and cage

(a) Computational domain

Section A0 Forward

direction Backward

direction

A1

B0

B1

(b) Grid of single bearing (c) Gird of matched mounting bearing Fig. 3 Computational domain and grid of angular contact ball bearing

⸘▚⚿ᨐߣ⠨ኤ

ゲฃߩ࿶ജ៊ᄬߦߟ޿ߡߪ㧘㕒࿶Ꮕࠍ↪޿ߡ⹏ଔߒߚޕ ᵹ㊂ଥᢙCߩቯ⟵ᑼߪ(1)ᑼߦ␜ߔㅢࠅߢ޽ࠅ㧘ሶඦ㕙ߢ ᦨ߽⁜޿ᢿ㕙A1㧔࿑3(b)㧕ࠍઍ⴫㕙Ⓧߣߒߚޕ

Ps

A C Q

2

1

U

ߎߎߢ㧘Q (m³/s)ߪ಄ළᵹ㊂㧘U _(kg/m³₎ߪᶧ૕ኒᐲ㧘'Ps

ߪ㕒࿶Ꮕߢ޽ࠆޕ

ゲฃ๟ࠅߩ಄ළᵹࠇߣ࿶ജ៊ᄬ

࿑4ߦゲฃන૕ߩ಄ළᵹࠇߩᵹ✢࿑ࠍ␜ߔޕߥ߅㧘ᵹ

✢ߪ₹ߩ౏ォߩ࿁ォ♽ߢ⴫␜ߒߡ޿ࠆޕ₹ߩ਄஥ߢߪ᷵

ࠍᏎߊᵹࠇ߇⊒↢ߒߡ޿ࠆޕߎࠇߪ଻ᜬེߩࡐࠤ࠶࠻ㇱ 㧔࿑ 3(a)㧕ߦ↢ߓߡ޿ࠆᵹࠇߢ޽ࠅ㧘਄ᵹࠃࠅࡐࠤ࠶࠻

ㇱߦ౉ࠅㄟࠎߛᵹ૕߇₹ߣ଻ᜬེߩ⁜޿㓗㑆ߢⶄ㔀ߥᵹ ࠇࠍ⊒↢ߐߖߡ޿ࠆޕ

࿑5ߦߪ 40000rpmߦ߅ߌࠆゲฃ๟ࠅߩㅦᐲࡌࠢ࠻࡞

࿑ࠍ␜ߔޕߥ߅㧘ㅦᐲࡌࠢ࠻࡞ߪ₹ߩ౏ォߩ࿁ォ♽ߢ⴫

␜ߒߡ޿ࠆޕ㗅ᣇะߢߪ₹ߩ⋧ኻᵹࠇߦኻߒߡ⢛㕙஥ߦ

᣿⏕ߥ෺ሶ᷵߇⊒↢ߒߡ߅ࠅ㧘৻⥸⊛ߥ⃿߿౞ᩇ๟ࠅߩ ᵹࠇߣหߓ᭽⋧ࠍ␜ߒߡ޿ࠆޕ৻ᣇ㧘ㅒᣇะߢߪᵹࠇߩ

೸㔌㗔ၞߪ޽ࠆ߇᣿⏕ߥ෺ሶ᷵ߪⷰኤߐࠇߥ޿ޕㅒᣇะ ߢߪ₹ߩ⢛㕙஥ߢౝベ߇⃿㕙ߦᴪߞߡᓢޘߦ⁜߹ࠆߚ߼㧘

ౝベ஥ߩᵹࠇ߇ඨᓘᣇะᄖ஥ߦะ߈ࠍᄌ߃ࠆޕߎߩᵹࠇ ߇෺ሶ᷵ߩ↢ᚑࠍᛥ೙ߒߡ޿ࠆ߽ߩߣផቯߐࠇࠆޕ ࿑ 6 ߦゲฃන૕ߩ࿁ォᢙߦኻߔࠆ࿶ജ៊ᄬߣᵹ㊂ଥᢙ ߩᄌൻࠍ␜ߔޕ߹ߚ㧘40000rpm ߦ߅ߌࠆ⚵วߖᑼゲฃߩ

⸘▚⚿ᨐࠍ৻✜ߦ␜ߔ߇㧘਄ᵹ஥ゲฃߣਅᵹ஥ゲฃߩਛ㑆

૏⟎ߢಽߌߡ㧘ߘࠇߙࠇߩ࿶ജ៊ᄬߣᵹ㊂ଥᢙࠍ⸘▚ߒߚޕ ࿁ォ㕒ᱛ㧔N = 0rpm㧕⁁ᘒߦ߅޿ߡߪ㧘㗅ᣇะߩᵹ㊂ ଥᢙߪCb0 = 0.699㧘ㅒᣇะߩᵹ㊂ଥᢙߪCb0 = 0.738ߢ޽

ࠆޕゲฃߩ࿶ജ៊ᄬߪ㗅ᣇะ߇ㅒᣇะࠃࠅ߿߿ᄢ߈޿߇㧘 㗼⪺ߥᏅ⇣ߪ⷗ࠄࠇߥ޿ޕߎߩᏅߪ㧘ᵹࠇᣇะߦࠃࠅᵹ

〝ߩ❗ዊ᜛ᄢߩࡄ࠲࡯ࡦ߇⇣ߥࠆߎߣ߿₹ߦᒰߚࠆ಄ළ ᵹࠇߩㅦᐲߣᒰߚࠆ㗔ၞߩ㆑޿ߦࠃࠆᓇ㗀ߣ⠨߃ࠄࠇࠆޕ ゲฃߩઍ⴫㕙Ⓧߣ╬ଔ㕙Ⓧߩࠝ࡝ࡈࠖࠬࠍ⠨߃ߚ႐ว㧘 JISⷙᩰ⁽⁵⁾ߢߪᵹ㊂ଥᢙߪC = 0.64ߢ޽ࠅ㧘ゲฃߩᵹ㊂ଥ ᢙߪࠝ࡝ࡈࠖࠬߦᲧߴߡᄢ߈޿௑ะࠍ␜ߔޕゲฃࠍㅢࠆ ᵹࠇ㧔࿑ 3㧕ߪⶄ㔀ߥᵹ〝ᒻ⁁ߢ޽ࠆ߇㧘ࠝ࡝ࡈࠖࠬߣ Ყߴߡ❗ዊㇱߦ޽ࠆ⒟ᐲߩ㐳ߐ߇޽ࠆߚ߼㧘࿶ജ៊ᄬߪ

ࠝ࡝ࡈࠖࠬࠃࠅዊߐߊߥࠆߎߣߪᅷᒰߥ⚿ᨐߢ޽ࠆߣ⠨

߃ࠄࠇࠆޕ

4 宇宙航空研究開発機構研究開発資料　JAXA-RM-11-013

FLOW

40000rpm 30000rpm

10000rpm

0rpm ^FLOW

40000rpm 30000rpm

10000rpm 0rpm

(a) Forward direction (b) Backward direction Fig. 4 Stream line through the angular contact ball bearing

Flow direction Flow direction

Revolution

direction Revolution

direction

Meridian velocity at section A1

11deg 21deg

Peripheral velocity

Meridian velocity at section B1

Peripheral velocity

(a) Forward direction (b) Backward direction (c) Velocity triangle Fig. 5 Velocity vector around bearing ball at 40000rpm

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0

0 10 20 30 40 50 60

0 10000 20000 30000 40000 50000

Flow coefficient Cb [-]

Pressure lossǻPb [kPa]

Revolution of shaft N [rpm]

Forward(Single) Backward(Single)

Upstream(Matched mounting) Downstream(Matched mounting)

Backward

Forward Forward

Backward

Fig. 6 Effect of bearing revolution on pressure loss and flow coefficient

࿁ォ㕒ᱛᤨߦߪᵹࠇᣇะߦኻߒߡ࿶ജ៊ᄬߦᭂ┵ߥ㆑޿

ߪ⃻ࠇߥ߆ߞߚ߇㧘࿁ォᢙ߇Ⴧടߔࠆߣ࿶ജ៊ᄬߩᄌൻ

௑ะߦᄢ߈ߥᏅ⇣߇↢ߓࠆޕ㗅ᣇะߩ႐ว㧘20000rpm߹ ߢ࿶ജ៊ᄬߪ૛ࠅᄌൻߒߥ޿߇㧘30000rpm ࠍ⿧߃ࠆߣ 20%⒟ᐲ៊ᄬ߇Ⴧടߔࠆޕ৻ᣇ㧘ㅒᣇะߩ႐วߪ㧘࿁ォ ᢙߩჇടߦኻߒߡ࿶ജ៊ᄬߪᷫዋߒ㧘40000rpmߢߪ࿶ജ

៊ᄬߪ0ߦㄭ޿୯ࠍ␜ߒߡ޿ࠆޕ

⚵วߖᑼゲฃߩ႐ว㧘਄ᵹ஥ߣਅᵹ஥ߩ࿶ജ៊ᄬߪන

૕ߢߩ⸘▚⚿ᨐߣ⦟ߊ৻⥌ߔࠆޕ਄ᵹ஥ゲฃߩ಴ญㇱߢ ߪ⚂0.3Zߩᣓ࿁ㅦᐲࠍᜬߞߡ޿ࠆ߇㧘ߘߩᣓ࿁ᵹࠇߪਅ ᵹ஥ゲฃߩ࿶ജ៊ᄬߦኻߒߡᓇ㗀߇ዊߐ޿ߎߣࠍ␜ߒߡ ߅ࠅ㧘⚵วߖᑼゲฃߩ࿶ജ៊ᄬߪゲฃන૕㗅ᣇะߣㅒᣇ ะߩ࿶ജ៊ᄬߩන⚐ߥ⿷ߒวࠊߖߢផቯߔࠆߎߣ߇น⢻

ߣ⸒߃ࠆޕ

ゲฃߩ࿶ജ៊ᄬߪ10kPaࠝ࡯࠳࡯ߢ޽ࠆߚ߼㧘ࡐࡦࡊ ല₸߿ࡃ࡜ࡦࠬࡇࠬ࠻ࡦ․ᕈߦኻߒߡߩᓇ㗀ߪዊߐ޿ޕ

FLOW

40000rpm 30000rpm

40000rpm 30000rpm

(a) Forward direction (b) Backward direction Fig. 4 Stream line through the angular contact ball bearing

Flow direction Flow direction

Revolution

direction Revolution

direction

Meridian velocity at section A1

11deg 21deg

Peripheral velocity

Meridian velocity at section B1

Peripheral velocity

(a) Forward direction (b) Backward direction (c) Velocity triangle Fig. 5 Velocity vector around bearing ball at 40000rpm

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0

0 10 20 30 40 50 60

0 10000 20000 30000 40000 50000

Flow coefficient Cb [-]

Pressure lossǻPb [kPa]

Revolution of shaft N [rpm]

Forward(Single) Backward(Single)

Upstream(Matched mounting) Downstream(Matched mounting)

Backward

Forward Forward

Backward

Fig. 6 Effect of bearing revolution on pressure loss and flow coefficient

࿁ォ㕒ᱛᤨߦߪᵹࠇᣇะߦኻߒߡ࿶ജ៊ᄬߦᭂ┵ߥ㆑޿

ߪ⃻ࠇߥ߆ߞߚ߇㧘࿁ォᢙ߇Ⴧടߔࠆߣ࿶ജ៊ᄬߩᄌൻ

௑ะߦᄢ߈ߥᏅ⇣߇↢ߓࠆޕ㗅ᣇะߩ႐ว㧘20000rpm߹ ߢ࿶ജ៊ᄬߪ૛ࠅᄌൻߒߥ޿߇㧘30000rpm ࠍ⿧߃ࠆߣ 20%⒟ᐲ៊ᄬ߇Ⴧടߔࠆޕ৻ᣇ㧘ㅒᣇะߩ႐วߪ㧘࿁ォ ᢙߩჇടߦኻߒߡ࿶ജ៊ᄬߪᷫዋߒ㧘40000rpmߢߪ࿶ജ

៊ᄬߪ0ߦㄭ޿୯ࠍ␜ߒߡ޿ࠆޕ

⚵วߖᑼゲฃߩ႐ว㧘਄ᵹ஥ߣਅᵹ஥ߩ࿶ജ៊ᄬߪන

૕ߢߩ⸘▚⚿ᨐߣ⦟ߊ৻⥌ߔࠆޕ਄ᵹ஥ゲฃߩ಴ญㇱߢ ߪ⚂0.3Zߩᣓ࿁ㅦᐲࠍᜬߞߡ޿ࠆ߇㧘ߘߩᣓ࿁ᵹࠇߪਅ ᵹ஥ゲฃߩ࿶ജ៊ᄬߦኻߒߡᓇ㗀߇ዊߐ޿ߎߣࠍ␜ߒߡ ߅ࠅ㧘⚵วߖᑼゲฃߩ࿶ജ៊ᄬߪゲฃන૕㗅ᣇะߣㅒᣇ ะߩ࿶ജ៊ᄬߩන⚐ߥ⿷ߒวࠊߖߢផቯߔࠆߎߣ߇น⢻

ߣ⸒߃ࠆޕ

ゲฃߩ࿶ജ៊ᄬߪ10kPaࠝ࡯࠳࡯ߢ޽ࠆߚ߼㧘ࡐࡦࡊ ല₸߿ࡃ࡜ࡦࠬࡇࠬ࠻ࡦ․ᕈߦኻߒߡߩᓇ㗀ߪዊߐ޿ޕ

ߦࠃߞߡ࿶ജ៊ᄬ߇ᭂ┵ߦᄌൻߔࠆߎߣ߆ࠄ㧘ዪᚲ⊛ߥ ᵹࠇߩ᭽⋧ߪᄢ߈ߊ⇣ߥߞߡ޿ࠆߎߣߪ࿑5߆ࠄ߽᣿ࠄ ߆ߢ޽ࠆޕߎߩᏅ⇣ߪゲฃ಄ළ․ᕈߦᄢ߈ߊᓇ㗀ࠍ෸߷

ߔߣ⠨߃ࠄࠇ㧘ߘߩࡔࠞ࠾࠭ࡓࠍ᣿ࠄ߆ߦߔࠆߎߣߪ㊀ ⷐߢ޽ࠆޕ

ᵹࠇᣇะߣ࿁ォᢙߦኻߔࠆ࿶ജ៊ᄬߩᏅ⇣ߦߟ޿ߡ

࿑7(a)ߦ0rpmߣ40000rpmߩᢿ㕙ᐔဋ㕒࿶ߩᄌൻࠍ㧘

࿑7(b)ߦ0rpmߣ40000 rpmߩᢿ㕙ᐔဋ㕒࿶ߩᏅߩᄌൻࠍ

␜ߔޕߥ߅㧘ゲฃ਄ᵹᢿ㕙㧔㗅ᣇะߢߪԘᢿ㕙㧘ㅒᣇะ ߢߪԤᢿ㕙㧕ߩ㕒࿶ࠍ0ߣߒߡᢛℂߒߚޕ

0rpmߢߪᦨ߽⁜޿ᢿ㕙A1ߢߩ❗ዊ᜛ᄢߦࠃࠆ࿶ജ៊

ᄬ߇ᡰ㈩⊛ߢ޽ࠆޕ40000rpmߢߪ㧘⋧ኻᵹࠇ߇₹߳ⴣ⓭ ߔࠆᢿ㕙ઃㄭ߹ߢ㕒࿶߇਄᣹ߒ㧘₹ߩ⢛㕙஥ߢ㕒࿶ߪ ᓢޘߦᷫዋߔࠆޕߘߒߡ଻ᜬེ߆ࠄਅᵹߦᵹࠇ಴ࠆ㗔ၞ

ߢ㕒࿶߇࿁ᓳߔࠆޕ

࿑7(c)ߦ㧘40000rpmߢߩᢿ㕙ᐔဋᣓ࿁ㅦᐲߩᄌൻࠍ␜

ߔޕߎߎߢᢿ㕙ᐔဋᣓ࿁ㅦᐲߪ㧘࿑7ߦ␜ߒߚฦᢿ㕙ߦ ߅ߌࠆᣓ࿁ㅦᐲಽᏓࠍ㕙Ⓧᐔဋߒߚ߽ߩߢ޽ࠆޕ₹ߩ౏

ォߦࠃࠅᣓ࿁ㅦᐲ߇਄᣹ߒ㧘ㅒᣇะߢߪߘߩᣓ࿁ㅦᐲࠍ ਅᵹ஥߹ߢ଻ᜬߔࠆ߇㧘㗅ᣇะߢߪ₹ߩ⢛㕙஥ߢᣓ࿁ㅦ ᐲ߇ᷫዋߔࠆޕߎࠇߪ࿑5(a)ߦ␜ߒߚ₹⢛㕙ߩᒝ޿෺ሶ

᷵߇ᣓ࿁ࠍᛥ೙ߒߡ޿ࠆߚ߼ߣ⠨߃ࠄࠇࠆޕ

એਅߦ࿁ォᤨߩᵹࠇᣇะߦࠃࠆ࿶ജ៊ᄬߩᏅ⇣ߩේ࿃

ߦߟ޿ߡ⠨ኤߔࠆޕ

㧔㧝㧕⋧ኻᵹࠇߩ₹߳ߩⴣ⓭ㇱߦ߅ߌࠆ㕒࿶਄᣹㧔㗅ᣇ ะԛ㨪ԝᢿ㕙㧘ㅒᣇะԡ㨪ԟᢿ㕙㧕㧦

⋧ኻᵹࠇ߇₹ߦⴣ⓭ߒߡ㕒࿶߇਄᣹ߒ㧘ㅒᣇะߢߪⴣ

⓭૏⟎ઃㄭߩԟᢿ㕙ߢ㕒࿶߇ࡇ࡯ࠢࠍ␜ߔ߇㧘㗅ᣇะߢ ߪⴣ⓭૏⟎ઃㄭߩԝᢿ㕙ߢᣢߦ㕒࿶߇ૐਅߒߡ޿ࠆޕ

ߓࠆޕᵹ✢߇ઍ⴫ඨᓘ㧔⥄ਸ਼ᐔဋ㧕ߢᄌൻߔࠆߣߒ㧘ᐔ ဋᣓ࿁ㅦᐲࠍ↪޿ߡ㆙ᔃജലᨐߦࠃࠆ࿶ജᏅࠍ⸘▚ߔࠆ ߣX1ߢߪ⚂5kPa޽ࠅ㧘ߎߩಽ߇㗅ᣇะߩԝᢿ㕙ߩ㕒࿶

ૐਅߩේ࿃ߣ⠨߃ࠄࠇࠆޕߥ߅㧘㆙ᔃജߦࠃࠆ࿶ജᏅ 'Pcenߪᣓ࿁ㅦᐲZ_r߇৻ቯߢ޽ࠆߣߒߡᰴᑼߦࠃࠅㄭૃ

⊛ߦ᳞߼ߚޕ

/

cen

dr r

dP U Z

2

2

P_{cen r} '

U Z

… (3)

㧔㧞㧕₹⢛㕙஥ߩ࿶ജ៊ᄬ㧔㗅ᣇะԝ㨪ԡᢿ㕙㧘ㅒᣇะ ԟ㨪ԛᢿ㕙㧕㧦

ᵹࠇߩ೸㔌ߦࠃࠆ࿶ജ៊ᄬߣ⠨߃ࠄࠇ㧘㗅ᣇะߢߪ࿑

5(a)ߦ␜ߔᒝ޿෺ሶ᷵ߩ⊒↢ߦࠃࠅᄢ߈ߥ࿶ജ៊ᄬ߇↢

ߓࠆߣផቯߐࠇࠆޕㅒᣇะߢ߽ᵹࠇߩ೸㔌ߪ⷗ࠄࠇࠆ߇㧘 㗅ᣇะߣᲧセߒߡ೸㔌ߩ㗔ၞߪዊߐߊ㧘࿶ജ៊ᄬ߽ዋߥ

޿ߣ⠨߃ࠄࠇࠆޕ߹ߚㅒᣇะߢߪ࿑8ߦ␜ߔౝベߦᴪߞ ߚY1 ߩᵹࠇߦࠃࠅ㆙ᔃജ߇௛߈㧘ߘߩ᣹࿶ಽ߇࿶ജ៊

ᄬߩૐᷫߦነਈߒߡ޿ࠆߣ⠨߃ࠄࠇࠆޕ೨ㅀߣห᭽ߦ⸘

▚ߔࠆߣ㧘᣹࿶ಽߪ⚂6kPaߢ޽ࠆޕ

㧔㧟㧕଻ᜬེ಴ญ߆ࠄਅᵹߢߩ㕒࿶࿁ᓳ㧔㗅ᣇะԡ㨪ԥ ᢿ㕙㧘ㅒᣇะԛ㨪Ԙᢿ㕙㧕㧦

ߎߩ㗔ၞ߽㆙ᔃജߦࠃࠆ᣹࿶ലᨐ߇௛޿ߡ޿ࠆߣ⠨

߃ࠄࠇࠆޕ࿑8ߦ␜ߔ଻ᜬེ಴ญ߆ࠄਅᵹ஥߳ߩᵹࠇ㧔X2㧘 Y2㧕ࠍ೨ㅀߣห᭽ߦ⸘▚ߔࠆߣ㧘㗅ᣇะߢߪ⚂7kPa㧘ㅒ ᣇะߢߪ⚂9kPaߩ᣹࿶߇↢ߓࠆޕᓥߞߡ㧘ߎߩ㗔ၞߢߩ 㕒࿶࿁ᓳߪ㆙ᔃജߦࠃࠆ᣹࿶ಽߦࠃࠅ߅߅ࠃߘ⺑᣿ߢ߈ ࠆޕ

6 宇宙航空研究開発機構研究開発資料　JAXA-RM-11-013

-50 -40 -30 -20 -10 0 10 20

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Mean static pressure Ps[kPa]

Position number

Forward䋺40000rpm Forward䋺0rpm Backward䋺40000rpm Backward䋺0rpm

Ball Cage Center

0rpm 40000rpm

0rpm 40000rpm

Backward

Forward

(a) Comparison of static pressure distributions

-20 -15 -10 -5 0 5 10 15 20 25 30

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Position number

Ball Cage Center

Backward

Forward

Mean static pressure differenceǻPs[kPa]

0 10 20 30 40 50 60 70 80

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mean tangencial component of velocity VT[m/s]

Position number

Forward Backward

(b) Static pressure difference between 0 and 40000rpm (c) Tangential component of velocity at 40000rpm Fig. 7 Distributions of mean static pressure and mean rotational speed

V_ș

=45(m/s)

V_ș

=54(m/s)

=41(m/s)

Y2 X2

Y1 V_ș

=48(m/s)

Fig. 8 Meridian flow and tangential component of velocity

◲ᤃࡕ࠺࡞ᑼߦࠃࠆ࿶ജ៊ᄬߩផቯ

࿶ജ៊ᄬ߿᣹࿶ലᨐߩේ࿃ផቯࠃࠅ㧘ゲฃߩ࿶ജ៊ᄬ ߪሶඦ㕙ᵹ〝ᒻ⁁ߦ⿠࿃ߔࠆ࿶ജ៊ᄬᚑಽߣ₹ߩ౏ォߦ

⿠࿃ߔࠆ࿶ജ៊ᄬ߅ࠃ߮᣹࿶ᚑಽߩ๺ߣߒߡࡕ࠺࡞ൻߔ ࠆߎߣ߇น⢻ߣ⠨߃ࠆޕ

ゲฃߩ࿶ജ៊ᄬ'Pbࠍ㧘ሶඦ㕙ᣇะߩ࿶ജ៊ᄬ'PM ߣ

ᣓ࿁ᵹࠇߩ㆙ᔃജߦࠃࠆ᣹࿶ലᨐಽ߽฽߻₹ߩ౏ォߦ㑐 ଥߔࠆ࿶ജ៊ᄬ'PCߩ๺ߣߒߡᰴᑼߢ⴫⃻ߔࠆޕ

2 2

02

2 2

䇭䇭䇭 ^M _{b b}

b C M b

V U C

P P P

D U

U

' ' '

… (4)

Forward

direction Backward

direction

㽴 㽵

㽶㽷 㽸㽹 㽺 㽳 㽻㽼 㽽

㽲 㽾

-50 -40 -30 -20 -10 0 10 20

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Mean static pressure Ps[kPa]

Position number Ball Cage Center

0rpm 40000rpm

0rpm 40000rpm

Backward

Forward

(a) Comparison of static pressure distributions

-20 -15 -10 -5 0 5 10 15 20 25 30

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Position number

Ball Cage Center

Backward

Forward

Mean static pressure differenceǻPs[kPa]

0 10 20 30 40 50 60 70 80

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mean tangencial component of velocity VT[m/s]

Position number

Forward Backward

(b) Static pressure difference between 0 and 40000rpm (c) Tangential component of velocity at 40000rpm Fig. 7 Distributions of mean static pressure and mean rotational speed

V_ș

=45(m/s)

V_ș

=54(m/s)

=41(m/s)

Y2 X2

Y1 V_ș

=48(m/s)

Fig. 8 Meridian flow and tangential component of velocity

◲ᤃࡕ࠺࡞ᑼߦࠃࠆ࿶ജ៊ᄬߩផቯ

࿶ജ៊ᄬ߿᣹࿶ലᨐߩේ࿃ផቯࠃࠅ㧘ゲฃߩ࿶ജ៊ᄬ ߪሶඦ㕙ᵹ〝ᒻ⁁ߦ⿠࿃ߔࠆ࿶ജ៊ᄬᚑಽߣ₹ߩ౏ォߦ

⿠࿃ߔࠆ࿶ജ៊ᄬ߅ࠃ߮᣹࿶ᚑಽߩ๺ߣߒߡࡕ࠺࡞ൻߔ ࠆߎߣ߇น⢻ߣ⠨߃ࠆޕ

ゲฃߩ࿶ജ៊ᄬ'Pbࠍ㧘ሶඦ㕙ᣇะߩ࿶ജ៊ᄬ'PM ߣ

ᣓ࿁ᵹࠇߩ㆙ᔃജߦࠃࠆ᣹࿶ലᨐಽ߽฽߻₹ߩ౏ォߦ㑐 ଥߔࠆ࿶ജ៊ᄬ'PCߩ๺ߣߒߡᰴᑼߢ⴫⃻ߔࠆޕ

2 2

02

2 2

䇭䇭䇭 ^M _{b b}

b C M b

V U C

P P P

D U

U

' ' '

… (4)

Forward

direction Backward

direction

㽴 㽵

㽶㽷 㽸㽹 㽺 㽳 㽻㽼 㽽

㽲 㽾

ߪ₹ߩ౏ォㅦᐲߢ޽ࠆޕD_bߪ₹ߩ౏ォߦ⿠࿃ߔࠆ࿶ജ៊

ᄬଥᢙߢ㧘⋧ኻᵹࠇ߇₹ߦⴣ⓭ߔࠆߎߣߢ↢ߓࠆ㕒࿶਄

᣹㧘₹⢛㕙஥ߢߩ೸㔌ߦࠃࠆ࿶ജ៊ᄬ㧘₹ߩ౏ォߢ↢ߓ ࠆᣓ࿁ᵹࠇߩ㆙ᔃജലᨐߦࠃࠆ࿶ജᄌൻߥߤࠍ฽ࠎߢ޿

ࠆޕCb0ߪ 0rpm ߢߩ CFD ⚿ᨐߢߩ୯ࠍ↪޿㧘D_bߪ

40000rpmߩCFD⚿ᨐࠃࠅวࠊߖㄟࠎߛ㧔㗅ᣇะ㧦D_b^㧩

0.07㧘ㅒᣇะ㧦D_b㧩㧙0.19㧕ޕ

࿑ 9 ߦ ࡕ ࠺ ࡞ ᑼ ߦ ࠃ ࠆ ⸘ ▚ ⚿ ᨐ ࠍ ␜ ߔ ޕ10000㨪

30000rpmߩCFD⚿ᨐߦኻߒߡ⺋Ꮕߪ⷗ࠄࠇࠆ߇㧘ో૕

⊛ߦ࿁ォᢙߦࠃࠆ࿶ജ៊ᄬߩᄌൻ௑ะࠍ⴫⃻ߢ߈ߡ޿ࠆޕ ߥ߅㧘⚵วߖᑼゲฃߩ႐วߪ㧘ゲฃන૕㗅ᣇะߣㅒᣇะ ߩ࿶ജ៊ᄬߩว⸘ߢផቯߔࠇ߫⦟޿ޕ

߽࿁ォᢙ਄᣹ߦ઻޿Ⴧടߔࠆޕ࿑10ߦ಄ළᵹ㊂߇࿁ォᢙ ߦᲧ଀ߒߡჇടߒߚ႐วߩ◲ᤃࡕ࠺࡞ᑼߦࠃࠆ࿶ജ៊ᄬ ߩᄌൻ௑ะࠍ␜ߔޕ࿁ォᢙ਄᣹ߦࠃࠆ಄ළᵹ㊂ߩჇടߦ ࠃࠅሶඦ㕙ᣇะߩ࿶ജ៊ᄬߪჇടߔࠆޕ৻ᣇ㧘࿁ォᢙߩ

਄᣹ߦࠃࠅਅᵹ஥㧔ㅒᣇะ㧕ߢߪ₹ߩ౏ォߦ㑐ߔࠆ᣹࿶

ലᨐ߇ᓧࠄࠇࠆߚ߼㧘ਅᵹ஥㧔ㅒᣇะ㧕ߩ࿶ജ៊ᄬߪ਄

ᵹ஥㧔㗅ᣇะ㧕ߣᲧߴߡ㕖Ᏹߦዊߐ޿ޕߘߩ⚿ᨐ㧘⚵ว ߖゲฃో૕ߩ࿶ജ៊ᄬߪ㧘߶ߣࠎߤ਄ᵹ஥㧔㗅ᣇะ㧕ߩ

࿶ജ៊ᄬᚑಽ߇භ߼ࠆߎߣߦߥࠆޕ

0 5 10 15 20 25 30 35 40

0 10000 20000 30000 40000

Pressure lossǻPb[kPa]

Revolution of shaft N [rpm]

ǻPc䋺Loss model CFD(Single)

CFD(Matched mounting upstream side) ǻP_M䋺Loss model

ǻP_M䋺Loss model

0 5 10 15 20 25 30 35 40

0 10000 20000 30000 40000

Pressure lossǻPb[kPa]

Revolution of shaft N [rpm]

ǻPc䋺Loss model CFD(Single)

CFD(Matched mounting downstream side) ǻP_M䋺Loss model

(a) Forward direction (b) Backward direction Fig. 9 Estimation of pressure loss (coolant flow rate = constant)

0 10 20 30 40

0 10000 20000 30000 40000

Pressure lossǻPb [kPa]

Revolution of shaft N [rpm]

Total Upstream side Downstream side Coolant flow rate QоN

Fig. 10 Estimation of pressure loss

(coolant flow rate о revolution)

8 宇宙航空研究開発機構研究開発資料　JAXA-RM-11-013

߅ࠊࠅߦ

ࡠࠤ࠶࠻↪࠲࡯ࡏࡐࡦࡊߦ↪޿ࠄࠇࠆࠕࡦࠡࡘ࡜₹ゲ ฃࠍኻ⽎ߦߒߚゲฃ಄ළᵹࠇߩCFD⸃ᨆࠍታᣉߒ㧘એਅ ࠍ᣿ࠄ߆ߦߒߚޕ

࡮࿁ォ㕒ᱛᤨߢߪ㧘ゲฃන૕ߢߩᵹ㊂ଥᢙߪ㗅ᣇะߢߪ Cb0 = 0.699㧘ㅒᣇะߢߪCb0 = 0.738ࠍ␜ߒߚޕゲฃߩ ᵹ㊂ଥᢙߪઍ⴫㕙Ⓧ߇╬ଔߥࠝ࡝ࡈࠖࠬߩᵹ㊂ଥᢙC

= 0.64ࠃࠅ߿߿ᄢ߈޿୯ࠍ␜ߔޕ

࡮ゲฃන૕ߢߪᵹࠇᣇะߦࠃࠅ࿁ォᢙߦኻߔࠆ࿶ജ៊ᄬ ߩᄌൻ߇⇣ߥࠆޕ₹ߩ౏ォߢ↢ߓࠆᣓ࿁ᵹࠇߦࠃࠆ㆙

ᔃജലᨐߣ₹⢛㕙ߩ೸㔌⁁ᴫߩ㆑޿ߦࠃࠆᓇ㗀ߣ⠨

߃ࠄࠇࠆޕ

࡮⚵วߖᑼゲฃߩ࿶ജ៊ᄬߪ㧘ゲฃන૕ߩ࿶ജ៊ᄬߩ⿷

ߒวࠊߖߦࠃࠅផቯߢ߈ࠆޕ

࡮ᣓ࿁ᵹࠇߦࠃࠆ㆙ᔃജലᨐߣ₹⢛㕙೸ࠍ⠨ᘦߒߚ◲ᤃ ߥࡕ࠺࡞ᑼࠍ૞ᚑߒ㧘ゲฃ࿶ജ៊ᄬߩ࿁ォᢙᓇ㗀ࠍ߅ ߅ࠃߘ⴫ࠊߔߎߣ߇ߢ߈ߚޕ

ෳ⠨ᢥ₂

(1) ଀߃߫㧘⿒᧻࡮᫪㧘Ꮏ૞ᯏ᪾↪ⅣႺኻᔕဳࠫࠚ࠶࠻

ẢṖࠕࡦࠡࡘ࡜₹ゲฃߩ㐿⊒㧘NTN TECHNICAL REVIEW㧘No.72㧔2004㧕㧚

(2) Kurokawa, J., et al., Axial Thrust Behavior in Lox-Pump of Rocket Engine, J. of Propulsion and Power, Vol.10, No.2(1994), 244-250.

(3) Subbaraman, M.R., et al., Bearing Coolant Flow Optimization, Advanced Earth-to-Orbit Propulsion Technology 1992, NASA CP 3174, Vol. II(1992), 439-449.

(4) ጟᧄ㧘ォ߇ࠅゲฃ: ߘߩ․ᕈߣታ↪⸳⸘㧘(1981)㧘 168-170㧘ᐘᦠᚱ㧚

(5) ᣣᧄᎿᬺⷙᩰ㧘JISZ8762-2 ౞ᒻ▤〝ߩ⛉ࠅᯏ᭴ߦࠃ ࠆᵹ㊂᷹ቯᣇᴺ㧙╙㧞ㇱ㧦ࠝ࡝ࡈࠖࠬ᧼㧘ᣣᧄⷙᩰ

දળ(2007).