㠽ข⋵↥ᬺᛛⴚ࠮ࡦ࠲࡯‫⎇ޓ‬ⓥႎ๔ͳ  ࡏ࡯࡞ࠛࡦ࠼ࡒ࡞ߩಾࠇ಺ᒻ⁁ߦ㑐ߔࠆ⎇ⓥ
Studies on Cutting Edge Geometry of Ball End Millsട⮮᣿Akira Katoࡏ࡯࡞ࠛࡦ࠼ࡒ࡞ߩಾࠇ಺ᒻ⁁ߪ‫⚻ޔ‬㛎ߦࠃࠅቯ⟵ߐࠇߡ޿ࠆ႐ว߇ᄙ޿‫ޔߒ߆ߒޕ‬ಾ೥ജߥߤߩᢙ୯⸃ᨆߦߪ‫ޔ‬ಾࠇ಺ᒻ⁁ߩቯ⟵߇ᔅⷐߢ޽ࠆ‫⎇ᧄޔߢߎߘޕ‬ⓥߢߪ‫ޔ‬᷹ቯߒߚಾࠇ಺ᒻ⁁ߩᐳᮡ୯ࠍ↪޿ߡ‫ޔ‬ಾࠇ಺ᒻ⁁ࠍቯ⟵ߒ‫ޔ‬ಾ೥ജߩ੍᷹ࠍⴕߞߚ‫ޕ‬Cutting edges of ball end mills are defined by experience in many cases. However, a definition of cutting edge geometry is needed for numerical analysis. Then, the cutting edge was defined using the value that measured the cuttingedge, and the cutting force was simulated.

 ߪߓ߼ߦ ࡏ࡯࡞ࠛࡦ࠼ࡒ࡞ಾࠇ಺ᒻ⁁ࡏ࡯࡞ࠛࡦ࠼ࡒ࡞ߪ‫⥄ޔ‬േゞ߿㘧ⴕᯏㇱຠߩ㊄ဳߩᎿౕ㗼ᓸ㏜ࠍ↪޿ߡ࿑㧝ߩᏒ⽼ߩࡏ࡯࡞ࠛࡦ࠼ࡒ࡞ࠃ߁ߥ‫ᦛޔ‬㕙ࠍ᦭ߔࠆㇱຠߩടᎿߦᐢߊ↪޿ࠄࠇࠆᎿ㧔⿥⎬‫ޔ‬ඨᓘ OO㧕ߩಾࠇ಺⒫✢ࠍ᷹ቯߒ‫⸃ޔ‬ᨆߔࠆౕߢ޽ࠆ‫ߩߎޕ‬Ꮏౕߪ‫ޔ‬ಾࠇ಺ߩ૏⟎ߦࠃࠅಾ೥ജ߇ߎߣߢಾࠇ಺ᒻ⁁ࠍᢙ୯ൻߒߚ‫ޔ߅ߥޕ‬᷹ቯᣇᴺߪᰴᄢ߈ߊᄌൻߔࠆ‫ޕ‬ಾ೥ജߪടᎿ⺋Ꮕ߿⴫㕙☻ߐ‫ޔ‬Ꮏౕߩߣ߅ࠅߢ޽ࠆ‫ޕ‬៺⠻ߣߩ⋧㑐߇㜞ߊ‫ޔ‬ಾ೥ജࠍផ᷹ߔࠆߎߣߪ‫ޔ‬ടᎿԘ 㨄㨅ᐔ㕙ߦ߅ߌࠆಾࠇ಺⒫✢ߩᐳᮡ୯ࠍ᷹ቯߒᕈ⢻ࠍ⹏ଔߔࠆߚ߼ߦ㊀ⷐߢ޽ࠆ‫ߦ⊛⥸৻ޔߒ߆ߒޕ‬ߚ‫ߩߟ৻ޔ߈ߣߩߎޕ‬ಾࠇ಺ߦߟ޿ߡ‫ޔ‬᷹ቯὐࡏ࡯࡞ࠛࡦ࠼ࡒ࡞ߩಾࠇ಺ᒻ⁁ߪ‫⚻ޔ‬㛎ߦࠃࠅቯ⟵ߐᢙߪ⚂  ὐߣߒߚ‫ޕ‬᷹ቯ⚿ᨐࠍ࿑㧞ߦ␜ߔ‫ޕ‬ࠇߡ߅ࠅ‫ޔ‬ಾࠇ಺ᒻ⁁ߩᢙ୯ൻ߇ⴕࠊࠇߡ޿ߥ޿ߎߣԙ ಾࠇ಺ߪ‫⃿ޔ‬਄ߦ㈩⟎ߐࠇࠆߎߣ߆ࠄ‫ޔ‬㨆ゲᐳ߆ࠄ‫ޔ‬ಾ೥ജߩផ᷹߇࿎㔍ߢ޽ࠆ‫ޕ‬ᮡ୯ࠍ㨄ゲ‫ޔ‬㨅ゲᐳᮡ୯ࠃࠅ⸘▚ߒߚ‫ޕ‬ߘߎߢ‫⎇ᧄޔ‬ⓥߢߪ‫࡞ࡒ࠼ࡦࠛ࡞࡯ࡏޔ‬ಾࠇ಺ᒻ⁁ࠍᢙ୯⊛ߦቯ⟵ߒ‫ޔ‬ಾ೥ജࠍផ᷹ߔࠆߎߣࠍ⹜ߺߚ‫ޕ‬4
㨅ゲ㧔mm㧕

2
0-2-4C ᄖⷰ      D ಾࠇ಺-402
㨄ゲ㧔mm㧕

࿑㧝 ࡏ࡯࡞ࠛࡦ࠼ࡒ࡞࿑㧞 ಾࠇ಺᷹ቯ⚿ᨐ

̶15̶

-24Ԛ ಾࠇ಺૏⟎ⷺǾߣಾࠇ಺ߨߓࠇⷺǫࠍ࿑㧟ߩࠃ߁ߦቯ⟵ߒ‫ޔ‬ԙߢ᳞߼ߚᐳᮡ୯ࠍᄌ឵ߒ‫ޔ‬ㄭૃ

k rc

W s sin( E  D e )sin I s cos(I s  E  D e )ktc

W s cos( E  D e )sin Is cos(Is  E  D e )ߔࠆߎߣߦࠃࠅ‫ޔ‬ಾࠇ಺ᒻ⁁ߩߨߓࠇࠍ␜ߔᑼ
㧔㧝㧕߅ࠃ߮࿑㧠ࠍ᳞߼ߚ‫ޕ‬ǫ㧩Ǿ㧞 Ǿ  㧔㧝㧕㧔㧟㧕ߐࠄߦ‫ޔ‬ᑼ㧔㧞㧕ߪᑼ㧔㧠㧕㧝㧕ߦᄌ឵ߢ߈ࠆ‫ޕ‬

 ℂ⺰⊛ಾ೥ᛶ᛫

 ³ I cos \ dF t  ³ I sin I sin \ dF r

Fx࿑㧡ߦ␜ߔࡏ࡯࡞ࠛࡦ࠼ࡒ࡞ಾࠇ಺ᓸዊⷐ⚛ߦ߅ߌ

³ I sin \ dF  ³ I sin I cos \ dF 㧔㧠㧕³ I cos I dFFy㧝㧕ࠆ‫ޔ‬ಾ೥ജ dFr ߅ࠃ߮ dFt ߪᑼ㧔㧞㧕 ߦࠃࠅ␜ߐࠇtFzrr

ࠆ‫ޕ‬ᑼ㧔㧝㧕߅ࠃ߮㧔㧠㧕ࠍ↪޿ߡ‫ޔ‬࿑㧝ߩࡏ࡯࡞ࠛࡦ

­dFr (\ ,I ) (kr  krc S (\ ,I ))rb dI   㧔㧞㧕®
¯dFt (\ ,I ) (kt  ktc S (\ ,I ))rb dI

࠼ࡒ࡞ߩಾ೥ജࠍᢙ୯⸃ᨆߒߚ‫⸃ޔ߅ߥޕ‬ᨆߦ↪޿ߚടᎿ᭎ⷐࠍ࿑㧢ߦ‫⸃ޔ‬ᨆߦ↪޿ߚቯᢙࠍ⴫㧝ߦ␜ߔ‫ޕ‬ߥ߅‫ߪ \ޔ‬Ꮏౕ࿁ォⷺ‫ ޔ‬k r ‫ ޔ‬k t ߪⵍ೥᧚ߦࠃࠅ᳿ⵍ೥᧚௑ᢳⷺߦߟ޿ߡߪ‫ޔ‬Ꮏౕవ┵ઃㄭߩಾࠇ಺߇ಾ

ቯߐࠇࠆଥᢙ‫ޔ‬S ߪಾࠅድෘߐ‫ޔ‬rb ߪᎿౕඨᓘߢ޽ࠆ‫ޕ‬೥ߦ㑐ਈߔࠆ௑ᢳⷺ q߅ࠃ߮‫ޔ‬Ꮏౕᄖ๟ઃㄭߩಾࠇ㧝㧕߹ߚ‫ޔ‬k rc ߅ࠃ߮ k tc ߪᑼ㧔㧟㧕 ߆ࠄዉ߆ࠇࠆ‫ޕ‬ᑼ㧔㧟㧕಺߇㑐ਈߔࠆ௑ᢳⷺ qߣߒߚ‫ޕ‬௑ᢳⷺ߇ qߩߣ߈ߩ D e ‫ ޔ‬E ‫ޔ‬I s ߪߘࠇߙࠇ᦭ലߔߊ޿ⷺ‫៺ޔ‬ᡂⷺ‫߅ޔ‬ߩ⸃ᨆ⚿ᨐࠍ࿑㧣ߦ‫ޔ‬qߩߣ߈ߩ⸃ᨆ⚿ᨐࠍ࿑㧤ߦࠃ߮ߖࠎᢿⷺߢ޽ࠆ‫ޕ‬␜ߔ‫ޕ‬㨆㨆㨄㨄㨅㨅ǾȀǫdFrǾಾࠇ಺⒫✢dFt ಾࠇ಺⒫✢࿑㧡 ࡏ࡯࡞ࠛࡦ࠼ࡒ࡞ಾࠇ಺ߩಾ೥ജ࿑㧟 ಾࠇ಺૏⟎ⷺǾߣಾࠇ಺ߨߓࠇⷺǫZY15ಾࠇ಺ߨߓࠇⷺ‫ޓ‬ǫq

X10ಾ ೥ᣇะ5௑ ᢳⷺ00ⵍ ೥᧚1020 30 40 50 60
ಾࠇ಺૏⟎ⷺ‫ޓ‬Ǿq70 ࿑㧠 ಾࠇ಺ߨߓࠇ૏⟎ⷺߣߨߓࠇⷺߩ㑐ଥ࿑㧢 ℂ⺰⸃ᨆߢ↪޿ߚടᎿ᭎ⷐ
̶16̶㠽ข⋵↥ᬺᛛⴚ࠮ࡦ࠲࡯‫⎇ޓ‬ⓥႎ๔ͳ   ⠨ኤ ߅ࠊࠅߦ ࿑㧠ߩࡏ࡯࡞ࠛࡦ࠼ࡒ࡞ಾࠇ಺૏⟎ⷺߣߨߓࠇⷺߩᧄ⎇ⓥߢߪ‫࡞ࡒ࠼ࡦࠛ࡞࡯ࡏޔ‬ಾࠇ಺ᒻ⁁ࠍ᷹ቯߒ‫ޔ‬㑐ଥࠃࠅ‫੹ޔ‬࿁᷹ቯߒߚᎿౕߪ‫ޔ‬ಾࠇ಺ߩߨߓࠇ߇‫ޔ‬ᢙ୯ൻߔࠆߎߣߦࠃࠅ‫ޔ‬ಾ೥ജࠍ⸃ᨆߒߚ‫੹ޕ‬ᓟߪ‫ޔ‬ࡏ࡯࡞ㇱ㗂ὐ߆ࠄᎿౕᄖ๟ߦ߆ߌߡ‫ޔ‬ᓢ‫ߦޘ‬Ⴧടߒߡ⸃ᨆ᧦ઙߩ᜛ᄢߣ‫ޔ‬ታടᎿߣߩᲧセࠍⴕ߁੍ቯߢ޽ࠆ‫ޕ‬޿ࠆߎߣ߇ࠊ߆ࠆ‫ޔࠄ߆ߣߎߩߎޕ‬ಾ೥ਛߦࡏ࡯࡞ㇱಾࠇ಺߆ࠄᓢ‫ߦޘ‬ᄖ๟ㇱಾࠇ಺߇ⵍ೥᧚ߦಾࠇㄟ߻ߎ⻢ ㄉߣ߇ࠊ߆ࠅ‫ޔ‬ಾ೥ജ߿ടᎿᾲߩ⊒↢߇✭߿߆ߥ߽ߩߣᧄ⎇ⓥࠍㆀⴕߔࠆߦ޽ߚࠅߏᜰዉ࡮ߏഥ⸒ࠍ޿ߚߛ

ߥࠆ‫ޕ‬߈߹ߒߚ‫ޔ‬࿖┙ᄢቇᴺੱ㠽ขᄢቇ ↰ਛਭ㓉ᢎ᝼ߦෘ ࿑㧣ߩ⚿ᨐࠃࠅ‫ⵍޔ‬೥᧚௑ᢳⷺ߇ qߢߪ‫ޔ‬ಾ೥ߦߊ߅␞↳ߒ਄ߍ߹ߔ‫⎇ᧄޔߚ߹ޕ‬ⓥߪ‫ޔ‬ᣣᧄ⥄ォゞᝄ㑐ਈߔࠆಾࠇ಺ߪᎿౕ࿁ォⷺ㧙㧝q߆ࠄq⒟ᐲߣᐢ

⥝ળ߆ࠄ┹ベߩ෼⋉㊄ߩ৻ㇱߢ޽ࠆᯏ᪾Ꮏᬺᝄ⥝⾗㊄▸࿐ߢ޽ࠆ‫ޔࠄ߆ߣߎߩߎޕ‬ಾࠇ಺ߦࠃࠆታಾ೥ᤨ㑆ߩ⵬ഥࠍฃߌߚ⸳஻ࠍ೑↪ߒߡ⎇ⓥߒߚ߽ߩߢߔ‫ޕ‬߇㐳ߊߥࠅ‫៺ࡉࠪ࠶࡟ࡉࠕޔ‬⠻߇ᄢ߈ߊߥࠆߣផ᷹ߐࠇࠆ‫ޔߚ߹ޕ‬ಾ೥ജ߇ዊߐߊಾ೥ജߩ⊒↢ߔࠆ࿁ォⷺᢥ ₂߇ᐢ޿ߎߣ߆ࠄ‫ⵍޔ‬೥᧚௑ᢳⷺ߇ዊߐ޿႐วߪ‫ޔ‬ಾࠅBERNAED W. IKUWA, HISATAKA TANAKA,

ድߪ⚦㐳޿ᒻ⁁ߦߥࠆߣផ᷹ߐࠇࠆ‫ޕ‬FUMIO ࿑㧤ߩ⚿ᨐࠃࠅ‫ޔ‬ಾ೥ജ㨅ゲᚑಽ㧲㨥߇࿑㧣ࠃࠅ߽

PREDICITION OF CUTTING FORCES AND⛘ኻ୯߇ᄢ߈ߊ‫ߩࠬ࠽ࠗࡑޔ‬ಾ೥ജߢ޽ࠆߚ߼‫ⵍޔ‬೥

MACHINING ERROR IN BALL END MILLING OF᧚௑ᢳⷺ߇ᄢ߈޿႐วߪ‫ޔ‬ಾࠅᱷߒߦࠃࠆടᎿ⺋Ꮕ߇

CORVEDᄢ߈޿ߎߣ߇ផ᷹ߐࠇࠆ‫ޕ‬

ANALYSIS, Precision Engineering, 25, P.269-270

OBATA,SATOSHISURFACES–1

SAKAMOTO;

THEORETICALಾ೥ജFx,Fy,Fz 㧺(2001).
⴫㧝 ℂ⺰⸃ᨆߢ↪޿ߚቯᢙⵍ೥᧚᧚⾰㧿㧷㧰㧝㧝㧔㧴㧾㧯㧕೻ᢿᒝߐǼ㨟 0OO ធ✢ജଥᢙǲV 0OOᴺ✢ജଥᢙǲT 0OOᎿౕ࿁ォⷺ‫ޓ‬Ǿ‫ޓ‬qǪq᧚⾰⿥⎬㧺ಾ೥ᎿౕᎿౕඨᓘ OO

ಾ೥ജFx,Fy,Fz៺ᡂⷺ࿑㧣 ⵍ೥᧚௑ᢳⷺ qߩℂ⺰⊛ಾ೥᦭ലߔߊ޿ⷺǩ㨑qಾ೥᧦ઙಾ೥ᣇะಾࠅㄟߺㅍࠅᎿౕ࿁ォⷺ‫ޓ‬Ǿ‫ޓ‬qࠕ࠶ࡊࠞ࠶࠻
ࠕ࠶ࡊࡇ࠶ࠢࡈࠖ࡯࠼
JHࡇ࠶ࠢࡈࠖ࡯࠼࿑㧤 ⵍ೥᧚௑ᢳⷺ qߩℂ⺰⊛ಾ೥ജ
̶17̶

 OO OOVQQJ
2H

 OO