模糊田口方法與面?刀具幾何形狀最佳化研究

዁ጙҤοПݲܻ७ሣΦڎඁդלޑശٹϽϞंـ

ଽ໌ᚌ! ዞٳݍ

ᓸ๼ऋ׬σᏰᐠడف

ᄢ! ौ

ҏंـ࢐ᔖҢҤοПݲ௤ଆ७ሣΦඁդלޑϛޟѲএкौُ࡙Ȉ৷ө༊

ُȃ໅ө༊ُȃᏲُڷΦቅј৷ޟᡐϽᄇϸࠈΨЅߒ७ಗ࡙ޟኇ៪ȂٮЕҢ዁

ጙ௰፣ݲᐌӫϸࠈΨᇄߒ७ಗ࡙ڍᆍࠢ፴੫ܒȂ௃Մײюኇ៪ϸࠈࠢ፴ޟᡗ๿

Ӱυоୈ࣏ΦڎശٹϽ೩ॎޟٷᐃȄᄂࢊПݲΰ஠ӑоಒӫޢҺߒϛӨᆍُ࡙

ಢӫޟ७ሣΦ໌՗ϸࠈᄂᡛȂ໔ڥϸࠈΨڷߒ७ಗ࡙о௤ଆኇ៪এտࠢ፴੫ܒ ޟ१ौӰυȂณࡣ஠ᄂᡛኵᐃϷտॎᆗܚுϞ߬ဴᚕॱШᏲΣ዁ጙ௰౩Пݲؑ

юфߒӻ१ࠢ፴੫ܒϞᒋ໔ࡾ኿ȞMPCIȟȂӔҥӰυਝݎϷݙЅᡐ౴ኵϷݙײ юӣਢኇ៪ΰक़ڍᆍϸࠈࠢ፴ޟᡗ๿ӰυȂശࡣӔԩ໌՗ᄂᡛᡛມശٹ୤ኵಢ ӫޟғጂܒȄϷݙ๖ݎᡗҰȂ७ሣΦඁդלޑѲএᒵۡޟџ௡ӰυϛϚ፣ᄇϸ ࠈΨܖߒ७ಗ࡙ܖڍޱӣਢຟեޟ௑ݷήȂ৷ө༊ُ࣏֯ᡗ๿ኇ៪ޟӰυȄ ᜰᗤຠȈ ७ሣȃҤοПݲȃΦڎඁդלޑȃӻ१ࠢ፴੫ܒȃശٹϽȄ

OPTIMIZATION OF TOOL GEOMETRY IN FACE MILLING OPERATION USING THE FUZZY-BASED TAGUCHI METHOD

Jin-Yih Kao! Ya-Dong Pan

Department of Mechanical Engineering Lunghwa University of Science and Technology

Taoyuan, Taiwan 333, R.O.C.

Key Words: face milling operation, Taguchi method, Tool geometry, Mul- tiple performance characteristics, Optimization.

ABSTRACT

The approach to optimize the cutter geometry through the use of fuzzy logics in the Taguchi method to deal with multiple performance character- istics is presented in this paper. Radial rake angle, axial rake angle, lead angle and nose radius are the optimized cutter geometric parameters when the performance characteristics, which include resultant cutting force and surface roughness in face milling operations, are taken into consideration.

An appropriate orthogonal array based on cutter geometric parameters is

selected for experiments to measure the performance characteristics. Then

the multiple performance characteristics index(MPCI) which merges two

performance characteristics is obtained after the individual signal-to-noise

ratio input the fuzzy logic unit. The results indicate that radial rake angle is

the most significant geometric parameter for affecting the multiple per-

formance characteristics.

Ιȃࠉ! ِ

७ሣࠈڎԤσ໔ಋଶ؅ਟޟ૖ΨȂҥܻᄂࢊᙏ൐иё ώਝ౥ଽٟϬϫ࢐Ңپפഀ౰ᇧيԁࠢ፴ҁ७ޟலҢП ݲȄஅҏΰ७ሣࠈ឴ܻၶፒᚕޟӻλϚ೿៉ϸࠈႆแȂϸ ࠈਢΦڎఋᙽᇄ໌๝ӣਢ໌՗Ȃϸৣᘞ७ԙೣࠌܒޟϚ೿

៉ᡐϽȂհҢӵሣΦΰޟϸࠈΨ֕౪໊෈ܒޟ׽ᡐȂԪᆍ

໊෈ܒޟϸࠈΨᡐϽඪټΟώڎᐠਏଢ଼ܚሯޟ૖໔௃Մኇ

៪ёώ७ޟߒ७ಗ࡙ȂܚоϸࠈΨޟσωЅёώ७ޟߒ७ ಗᕹแ࡙ϚѶ࣏ຟե७ሣࠈёώࠢ፴ᓺӛޟԤਝࡾ኿ȄΙ ૡՄِȂ࣏׽๡७ሣᇧแޟࠢ፴σഋӋޟंـ֯๿ಁܻϸ

ഀȃϸ౏ȃ໌๝้ϸࠈనӇޟ௡ڙ[1-4]ȂณՄ௃७ሣΦڎ

ඁդלޑޟ፣ᘈ௤ଆ७ሣᇧแࠢ፴ޟ׽๡ਝݎࠌЍԤڎᡝ ๖ݎ֕౪Ȅ

ජक़७ሣΦڎඁդלޑޟ१ौُ࡙Ԥ৷ө༊ُȞradial rake angle, ͗ nm ȟ ȃ໅ө༊ُȞaxial rake angle, i m ȟ ȃᏲُȞlead angle, C sm ȟȃΦቅј৷Ȟnose radius, rȟȃΦᆒُЅሪُ้ȇ Өُ࡙ޟհҢΙૡ࢐۽៉ᄇٙࠈΦڎޟᇯޣ[5]ȂࠉѲޱޟ

׽ᡐ஠ོኇ៪ϸৣӵΦ७ΰޟࢺଢ଼ПөЅഀ࡙໌Մഅԙϸ ࠈΨޟᡐϽ[6]Ȃࡣڍޱࠌкौ࢐ՃኌΦڎڷώӇޟኞᔢհ ҢȂӨُ࡙ޟ೩ॎζ҆໸ঙ៫ڗϸλޟ஼࡙Ȅ୦ཾϽޟ७ ሣΦ೽லོᄇ੫ۡ؅ਟ௰ᙨ࢚ٲُ࡙ಢӫȂծᒵᐅ၎ಢӫ ޟনӰΝՍܻ၎ಢӫ࢐֏࣏ശٹϽܖߖխശٹϽٮϚுՄ ޣȇӰԪᒵᐅᎌ࿋ޟࠢ፴੫ܒ஠Өُ࡙ޟհҢ௑לёо໔ ϽȂ໌Մ஠ඁդלޑ୤ኵޟϷݙ๖ݎᏲΣ७ሣΦڎޟശٹ Ͻ೩ॎȂࣺ߬ᄇ७ሣᇧแࠢ፴ޟ׽๡஠࢐१ौՄԤཎဎޟȄ

ҏМ஠ᔖҢҤοПݲȞtaguchi methodȟᄇ७ሣΦڎޟ לޑ໌՗୤ኵ೩ॎȂ௤ଆ৷ө༊ُȃ໅ө༊ُȃᏲُЅΦ ቅј৷้Ѳএџ௡ӰυȞcontrol factorsȟᄇሣࠈႆแϛϸ ࠈΨڷώӇߒ७ಗ࡙ڍএࠢ፴੫ܒޟኇ៪ȂٮЕҢ዁ጙ௰

፣ݲᐌӫԪᚖ१ࠢ፴੫ܒᡐԙ൐Ιࠢ፴੫ܒޟᒋ໔ࡾ኿Ȃ კၐ௃Φڎלޑ൶ؑኇ៪ϸࠈࠢ፴ޟᡗ๿Ӱυоୈ࣏Φڎ ശٹϽ೩ॎޟٷᐃȄ

ҤοПݲ࢐Ιᆍђ૖஼σޟᄂᡛ೩ॎПݲ[7]ȂѺᄇ౰

ࠢޟܒ૖ڷࠢ፴ޟശٹϽ೩ॎඪټΙᆍᙏ൐ԤਝиفಛϽ ޟंـഊ৷ȇആႆҤοПݲ୤ኵ೩ॎܚுϞᇧแ୤ኵџٺ

ࠢ፴੫ܒႀڗശᎌϽиٺفಛߒ౪ᄇᡐ౴پྛޟఃཐ࡙६ ճȄҤοПݲޟ੫Փ࢐ցҢޢҺߒ೩ॎᄂᡛȂџפഀȃင ᔼӴӣਢंـӻএџ௡Ӱυᄇࠢ፴੫ܒҁ֯঄Ѕᡐ౴ኵϞ ኇ៪Ȅҥᄂᡛኵᐃܚᙽᡐޟ߬ဴᚕॱШȞsignal-to-noise ratio, S/N Шȟ଩ӫᡐ౴ኵϷݙȞanalysis of variance, ANOVAȟ џሆܾӴײюџ௡Ӱυޟശᎌ୤ኵЫྥಢӫٮᒱᜋюኇ៪

ࠢ፴੫ܒޟᡗ๿ӰυȄԪѴȂ࣏ᐌӫϸࠈΨڷߒ७ಗ࡙ڍ ᆍϚӣޟࠢ፴੫ܒȂҏМ஠ЕҢ Tarng[8]้Ρܚี৤Ϟڎ Ԥ዁ጙܒ೩ॎҬ኿ޟӻ१ࠢ፴੫ܒᅋᆗݲȂоএտࠢ፴੫ ܒޟ S/N Шୈ࣏዁ጙݲࠌޟᒯΣᡐኵȂՄоӻ१ࠢ፴੫ܒ Ϟᒋ໔ࡾ኿Ȟmultiple performance characteristics index,

ყ 1! ७ሣΦޟඁդלޑ

MPCI ȟ࣏ڏᒯюᡐኵȂณࡣо MPCI ໌՗ӰυਝݎϷݙЅ ᡐ౴ኵϷݙȂ௃ՄᕕுΦڎඁդלޑϛኇ៪ϸࠈΨڷߒ७ ಗ࡙ڍᆍࠢ፴੫ܒޟᡗ๿ӰυȄശࡣӵശᎌಢӫޟనӇή

໌՗ᡛᜌᄂᡛٮ஠๖ݎᇄႱก঄Шၶоրۡёݲ዁Ԓ࢐֏

ԙҳȄ

Πȃ७ሣᇧแ

७ሣΦ࢐ӵ༫לΦዺ၆೩Ιএܖӻএϸλޟଟᙽϸࠈ ΦڎȂΦλఋᙽٮᇄಋଢ଼ϛޟώӇհ໢ྐܒޟㇵΣоಋଶ

؅ਟȇଽਝ౥ޟёώ૖Ψ࢐ٺڏӵҁ७ёώПݲࡻ៉ڧڗ १ຜޟശσ੫ᘈȂծӰᘞ៉ԒޟϸࠈПԒٺுϸλܛڧ໊

෈ܒޟፐᔞȂܾЕีІ᙭ᔖΨᏲमΦڎᓹນܖᐭีϸࠈᠬ ਏȞChatterȟȂϚծёώ७ޟಗᕹ࡙ቨёᄇᐠᏢҏᡝζԤϚ يޟኇ៪Ȅ

ყ 1 ܚҰ࣏७ሣΦޟඁդלޑȂ७ሣΦޟؐΙএϸλ џຜ࣏ΙЛٙΦȂӵඁդלޑΰӨُ࡙ޟۡဎڷհҢζԤ ڏࣺᜰܒȄყϛܚҰȂ࿋ϸ౏ᇄ໌๝໔ھۡਢȂᏲُᡐσ ϸৣޟࠔོ࡙ᡐᖡٺϸλΰ൐՝ߝ࡙ޟϸࠈΨ෵ЍȂծЊ σޟᏲُᡱϸৣቶ࡙ቨёІٺϸࠈΨᡐσȇ೩ॎு࿋ޟᏲ

ُϚ༉џЕᏲϸৣ໷ᄱ௶ଶиџ஠ϸࠈΨᎌ࿋Ϸ၌ȂԤօ

ܻ௡ڙϸࠈᠬଢ଼ඪଽёώߒ७ޟࠢ፴Ȅ৷ө༊ُᄇϸৣࢺ ଢ଼ȃϸλ஼࡙ЅϸࠈΨσωޟᜰ߽ၶ஝ϸȄၶσޟ৷ө༊

ُלԙᎠցޟλοٺϸৣࢺଢ଼໷ᄱȂџ६ճϸࠈߢΨЅ׻

ڙΦοᑖৣȞBUEȟޟีҡȂџ࢐Њσޟ৷ө༊ُࠌٺΦ λ஼࡙६ճȂλοৠܾ஫ນȂӰԪᄇܻ฽፴؅ਟܖᘞ៉ϸ ࠈ৷ө༊ُல௴Ңُ॒೩ॎȂԪᆍПԒᗶོٺϸৣלԙᔠ ᔆ౪ຫȂቨёଢ଼ΨੑẑȂծӵ஼σޟϸࠈߢתή٩Хλο

஫ཬޟਝݎሳٹȄ७ሣΦޟ໅ө༊ُᄇܻϸৣࢺଢ଼Ѕϸࠈ

Ψσωޟਝᔖᇄ৷ө༊ُሳ࣏ࣺխȂሯݧཎޟ࢐॒ޟ໅ө

ყ 2! հҢӵ७ሣΦ࢚ΙλΰޟϸࠈΨϷ໔

༊ُᗶџٺ஼࡙ቨёȂծϸৣೝࠉ༊ޟΦ७܁ήᔆৠܾژ

༌ёώ७ȄΦቅј৷ᄇ७ሣΦϸλ஼࡙ڷёώ७ಗᕹ࡙ኇ

៪࢐ΪϷ१ौޟȂष൷έُלΦλپ௤ଆΦቅј৷ޟਝ ᔖȂј৷ЊωࣥՍ࢐ԌᎠޟΦԌ஠ོӵёώ७לԙಠ஝ޟ ΦԌ౷ၬٺߒ७ಗᕹ࡙ቨёȂՄϸࠈᔖΨ໱ϛζ஠ٺΦԌ

஫ཬȇІϞၶσޟΦቅј৷ٺλο஼࡙ᡐσȂϸࠈᔖΨϷ շܻၶσޟቅᆒΰΦԌၶϚܾཬᚽȂёώ७ޟಗᕹ࡙ζࣺ

ᄇ६ճȂϚႆј৷Њσࠓџ૖ЕଔΦڎᎪଢ଼Ȅ

ყ 2 ࣏७ሣࠈਢ಑ i λӵ࢚Ιᕡ໢ᙽڗُ՝ည͞ i ਢϸ λܚܛڧޟϸጣհҢΨ F _mt

_i

ȃ৷өհҢΨ F ڷ໅өհҢ _mr

_i

Ψ F _mv

_i

Sm R Sm T mv

Sm R Sm T mr

C mt

C F C F F

C F C F F

F F

i i

i

i i

i i i

cos sin

sin cos

−

=

+

=

=

(1)

ڏϛ F C фߒғҺϸࠈ዁࠮ϛᇄϸλಋଢ଼ПөࣺІȂհҢӵ ϸλΰޟϸࠈΨ

F T фߒ࠭ޢ F C Ѕϸࠈߒ७ޟϸࠈΨ F R фߒ࠭ޢ F C Ѕ F T ޟϸࠈϷΨ

௃ Young[6]Ѕ Wang[9]ޟंـᡗҰȂΦڎלޑٺϸৣ

ቶ࡙ȃࠔ࡙ЅϸৣࢺငΦ७ޟഀ࡙ЅПө֕౪Ϛӣޟᡐ ϽȂϸࠈΨζӰՄԤܚ৯౴Ȅყ 3 ܚҰȂ஠հҢӵ಑ i ϸ λޟϸࠈΨϷ၌ڗ XȃYȃZ έএПөΰࠌڏΨ໔࣏

i i

i i

i

i i

i

mv Z

i mr i mt Y

i mr i mt X

F F

F F

F

F F

F

=

+

=

−

=

θ θ

θ θ

sin cos

cos sin

(2)

ϸ ࠈ ႆ แ ϛ џ ૖ Ԥ ኵ λ ӣ ਢ ໌ ՗ ϸ ࠈ Ȃ ࢈ о ᠒ ё ݲ ȞsuperpositionȟپॎᆗհҢӵΦڎΰ XȃYȃZ ӨПөޟ ᕡਢϸࠈΨᖂڷ

∑

∑

=

=

=

=

t i t

i

N

i Y i

Y N

i X i

X

F i F

F i F

1 1

) ( ) (

) ( ) (

θ δ

θ δ

ყ 3! Ґᡐלϸৣࠔ࡙ᇄϸࠈΨޟᜰ߽

∑ =

= ^N

^t _i

i Z i

Z i F

F 1 δ ( ) ( θ )



 

 ≤ ≤

= 0 ࠡה

ૉ ) 1

( i θ ^e θ ⁱ θ ^f

δ ⁽³⁾

N ࣏Φλኵ t

θ e ࣏໌Σُ

θ f ࣏ଝюُ

о XȃYȃZ έ໅өޟᕡਢϸࠈΨॎᆗϸࠈΨᖂӫџு

2 2

2 Y Z

X F F

F

F = + + (4)

ᆣӫΰक़Ȃ७ሣΦڎ೩ॎџٷܚ೩ۡޟђ૖Ҭ኿ᙤҥלޑ ޟ፡ᐌپቨёϸλޟ஼࡙ȃЕᏲϸৣ௶ଶȃ׽ᡐϸৣלޑȃ ६ճϸࠈΨඪଽϸࠈᛧۡܒȂᗗջӰਏΦܖϸλҏ٘ޟל ޑཬЅёώ७ޟಗᕹ࡙ȄӵھۡޟϸࠈనӇᇄࣺӣޟᕗც ήȂϸࠈΨσωЅёώ७ޟಗᕹ࡙࢐Φڎϸࠈޟᆣӫߒ ౪Ȃؐএُ࡙ᗶӨԤڏհҢծܚլӋ໔ࠓϚᅾࣺӣȂӰԪ

୲Ԥ࡚ҳׇᐌޟ໔Ͻၥਟϗ૖ඪټΦڎ೩ॎਢޟ୤Ճٷ ᐃȄ

έȃᄂ! ᡛ

ҏंـޟҬޟӵᙤҥҤοᄂᡛϛޟ୤ኵ೩ॎپ௤ଆ७ ሣΦඁդלޑᄇϸࠈࠢ፴ޟኇ៪ਝݎȄҥܻϸࠈΨЅёώ ७ޟߒ७ಗᕹ࡙џԤਝІᔖᐌᡝϸࠈࠢ፴ޟߒ౪Ȃ໔Ͻޟ

ႆแၶৠܾȃܚு๖ݎࡊᢎиڎ୤Ճܒ࢈ᒵᐅԪΠޱ࣏ࠢ

፴੫ܒӰυȂڏтࣺᜰޟӰશ፝ԃϸ౏ȃϸഀȃ໌๝้ࠌ

஠Ϡоھۡٮ၏ӖܻࡣȄ

ߒΙ! S45C ϛᆇᓁϽᏰԙӋЅᐠడܒ፴ ϽᏰԙӋ(%) ६Ӆ஼࡙

(MPa) 340 C P Mn Si Cr Ni תܜ஼࡙

(MPa) 560 0.45 0.17 0.76 0.17 0.032 0.04 ࠏЪ฽࡙ 137~170

ყ 4! ϸࠈΨ໔ก၆ည

1.ᄂᡛ೩രᇄώӇ؅ਟ (1) ϸࠈΨᄂᡛ೩ര

ϸࠈΨᄂᡛ೩രϞ଩ညԃყ 4 ܚҰȂڏϛѓ֤྆១ MV-3A ᆣӫёώϛЖᐠȃKistler 9255B έ໅өଢ଼Ψॎ

Ѕ 5007 Ⴋ೉ܹσᏢȃEasyster A/D ଉဴᙽ඲ЅϷݙ೺

ᡝȄ

(2) ߒ७ಗᕹ࡙໔ก

РҏέᙴȞMitutoyoȟ Surf-301 ߒ७ಗ࡙ቈȄ (3) ώӇ؅ਟᇄ७ሣΦޟೣਿ

ώӇ؅ਟ௴Ң S45C ϛᆇᓁȂڏϽᏰԙӋЅᐠడܒ፴ ԃߒΙȄ

(4) ७ሣΦ

ޢ৷ 125mm Ϟ७ሣΦЅӨᆍޟΦ࢜ȂؐΙᆍΦ࢜ޟ

ُ࡙ಢӫ࢐ٷޢҺߒޟሯؑپᇧհȂ௻ణԒΦа࣏

P17 ᜸ሪُ 11 ^o ϞέُלฒᗡቹᆇϽސΦаȄ 2.ᄂᡛПݲ

(1) ϸࠈΨ໔ก

ӵھۡޟϸ౏ȃϸഀЅ໌๝้నӇήٷޢҺߒܚӖϞ

ؐΙᆍלޑ୤ኵಢӫ໌՗ϸࠈᄂᡛȂϸࠈΨޟଉဴആ

ႆၥਟᘝڥفಛԆܻႫသϱȄ࣏Ο௶ଶӻλϸࠈܚ౰

ҡޟ୑ᘛȞRunoutȟ୰ᚠٺϸࠈΨଉဴጂᄂІᔖΦڎ לޑޟਝݎ࢈௴൐λϸࠈȄϸࠈనӇӖक़ԃήȈ ϸഀȈ250 m/minȄ

ϸ౏Ȉ໅өϸ౏࣏ 4mmȂ௴Ӓ৷өϸࠈȞfull immer- sion ȟȄ

໌๝໔Ȉ0.1 mm/toothȄ

ߒΠ! џ௡ӰυЅڏЫྥ

ಒဴ לޑ୤ኵ ൐՝ Ыྥ 1 Ыྥ 2 ȁ Ыྥ 3 B ৷ө༊ُ ࡙ -6* 0 6 C ໅ө༊ُ ࡙ -6 0 6*

D Ᏺ! ! ُ ࡙ 0 15 45*

E Φቅј৷ mm 0.4 0.8 1.2*

* ࣏ଔۖלޑ୤ኵ

ଉဴڥኺᓜ౥Ȟsampling rateȟȈ400HzȄ (2) ߒ७ಗ࡙໔ก

ӵؐԩϸࠈׇԙࡣ։оߒ७ಗ࡙ቈညܻёώ७ΰ໔ڥ ಗᕹ࡙Ȃ௤ᓞಋଢ଼Пө໸࠭ޢܻϸࠈ઴ၯȂߒ७ಗ࡙

঄ޟຟեݲ࢐௴ҢϛЖጣҁ֯ಗᕹ࡙ȞRaȟȂ൐՝͢

m Ȃᄠᘞ঄ڥ 0.8mmȄ 3.Ҥοᄂᡛ

ҏंـ߽о७ሣΦϸࠈϛᆇᓁޟϸࠈӫΨσωЅёώ ७ޟಗᕹ࡙࣏ࠢ፴੫ܒӰυȂڍޱ֯឴ఖω੫ܒȞthe small the better ȟȄ७ሣΦڎלޑϛޟ৷ө༊ُȃ໅ө༊ُȃᏲُ

ЅΦቅј৷Ѳএُ࡙ࠌ࣏џ௡ӰυȂؐএӰυࣱ೩έএЫ

ྥȂӨЫྥޟ೩ۡ࢐୤Ճѿ୵७ሣΦலَޟُ࡙೩ॎȂڏ ϛ৷ө༊ُȃ໅ө༊ُӨڥ-6 ^o ȃ0 ^o ȃ6 ^o ࣏ڏέЫྥȂϷտ фߒُ॒ȃႭُЅғُΦȇџ௡ӰυЅڏЫྥԃߒΠܚҰȄ ҥܻԤ 4 এџ௡ӰυȂؐএӰυࣱԤ 3 এЫྥȂငᒋ໔џ

௡Ӱυڷᇲ৯ޟՌҥ࡙о L 18 ޢҺߒၶӫᎌȂԃߒέܚҰȇ һ։ΦڎלޑޟᄂᡛనӇԤ 18 ᆍಢӫȂ࣏ؑᄂᡛޟྥጂܒ

ؐΙᆍᄂᡛ१᙭໌՗ 3 ԩȂᄂᡛܚ໔ڥϞϸࠈΨЅߒ७ಗ

࡙஠Ϸտೝᙽ඲ԙ S/N Шо໌՗ᡐ౴ኵϷݙоؑுএտࠢ

፴੫ܒޟശᎌЫྥಢӫٮᒱᜋюᡗ๿ӰυȄӵӣਢՃኌϸ ࠈΨЅߒ७ಗ࡙ᚖ१ࠢ፴੫ܒ୰ᚠޟ೎౩ΰΝ࢐װڍޱএ տࠢ፴੫ܒޟ S/N Шୈ࣏዁ጙ௰౩فಛޟᒯΣᡐኵȂငҥ ܚ࡚ҳޟ዁ጙ௰౩ೣࠌၼᆗࡣофߒӻ१ࠢ፴੫ܒޟᒋ໔

ࡾ኿Ȟmultiple performance characteristics index, MPCIȟ࣏

ڏᒯюᡐኵȇᄇ MPCI ໌՗ӰυਝݎϷݙЅᡐ౴ኵϷݙ߯

џᕕுӣਢኇ៪ᚖ१ࠢ፴੫ܒޟശᎌЫྥಢӫЅᡗ๿Ӱ υȂശࡣӔ໌՗ᡛມᄂᡛጂᇯᄇԪᚖ१ࠢ፴੫ܒޟຟեਝ ݎȄ

Ѳȃ๖ݎᇄଆ፣

1.൐Ιࠢ፴੫ܒȞϷտՃኌϸࠈΨЅߒ७ಗ࡙ȟ ७ሣёώਢϸࠈΨཕωཕԁȂ࢈ࠢ፴੫ܒ࢐௴Ңఖω ੫ܒޟ୤ኵ೩ॎȇߒѲ࣏ϸࠈᄂᡛܚுϞϸࠈΨޟҁ֯

঄Ȃᡐ౴ኵЅ S/N ШȄ௃ߒϤ S/N ШӱᔖߒџޣϸࠈΨ࣏

ശωޟശᎌЫྥಢӫ࣏ B3C1D2E1Ȃ։৷ө༊ُ 6 ^o ȃ໅ө

༊ُ-6 ^o ȃᏲُ 15 ^o ЅΦቅј৷ 0.4mmȄߒϲ࣏ᡐ౴ኵϷݙ

ߒέ! לޑ୤ኵЫྥȞL 18 ޢҺߒᇄӰυ଩ညȟ

ᄂᡛ A B C D E

ጡဴ ᇲ৯ ৷ө༊ُ ໅ө༊ُ Ᏺُ Φቅј৷

1 1 1 1 1 1

2 1 1 2 2 2

3 1 1 3 3 3

4 1 2 1 1 2

5 1 2 2 2 3

6 1 2 3 3 1

7 1 3 1 2 1

8 1 3 2 3 2

9 1 3 3 1 3

10 2 1 1 3 3

11 2 1 2 1 1

12 2 1 3 2 2

13 2 2 1 2 3

14 2 2 2 3 1

15 2 2 3 1 2

16 2 3 1 3 2

17 2 3 2 1 3

18 2 3 3 2 1

ߒѲ! ϸࠈΨޟ S/N Ш

ᄂᡛጡဴ ҁ֯঄(N) ᡐ౴ኵ S/N (dB) 1 486.490 5.190 -53.742 2 427.807 10.698 -52.625 3 542.227 53.728 -54.684 4 473.713 75.755 -53.511 5 437.500 154.630 -52.822 6 526.193 208.152 -54.425 7 314.793 68.300 -49.963 8 485.443 102.607 -53.724 9 397.967 147.203 -52.000 10 534.127 6.012 -54.553 11 529.867 275.824 -54.486 12 502.700 164.520 -54.028 13 434.167 29.703 -52.754 14 499.133 23.963 -53.965 15 448.200 38.430 -53.030 16 460.867 76.223 -53.273 17 421.000 1.96 -52.486 18 389.800 55.870 -51.818

ޟ๖ݎȂڏϛ৷ө༊ُڷᏲُޟ F ঄Ϸտ࣏ 12.19ȃ11.24Ȃ ଓᝦ࡙Ϸտ࣏ 42.15%Ѕ 38.85%ȂӰԪրᘞ৷ө༊ُڷᏲ

ُ࣏ኇ៪ϸࠈΨσωޟᡗ๿ӰυȂܚоӵհശᎌЫྥή S/N ШϞեॎਢѫՃኌԪڍӰυޟਝᔖȄߒΜܚҰ࣏ӵശ ᎌనӇήШၶ S/N ШϞᄂᡛ঄Ȟ-49.963dBȟᇄႱก঄

Ȟ-51.329 dBȟȂ๖ݎᡗҰڍޱࣺ৯࡞ωȂ࢈џᇳ݂ёݲ዁

ߒϤ! ϸࠈΨޟ S/N Шӱᔖߒ ಒဴ לޑ୤ኵ S/N Шҁ֯঄ (dB)

Level 1 Level 2 Level 3 Max-Min B ৷ө༊ُ -54.020 -53.418 -52.210 1.809 C ໅ө༊ُ -52.966 -53.351 -53.331 0.386 D Ᏺ! ! ُ -53.209 -52.335 -54.104 1.769 E Φቅј৷ -53.066 -53.365 -53.216 0.299

S/N Шᖂҁ֯঄ɶ-53.216 (db)

ߒϲ! ϸࠈΨޟ S/N Шޟᡐ౴ኵϷݙ

ಒဴ לޑ୤ኵ Ռҥ࡙ ҁПڷ ֯Пڷ F ঄ ! ଓᝦ࡙(%) B ৷ө༊ُ 2 10.187 5.094 12.193 42.150 C ໅ө༊ُ 2 0.565 0.282 0.676 2.336 D Ᏺ! ! ُ 2 9.389 4.695 11.238 38.848 E Φቅј৷ 2 0.268 0.134 0.321 1.109 ᇲ৯ 9 3.760 0.418 15.556 ᖂڷ 17 24.168 100

ߒΜ! ϸࠈΨϞଔۖЫྥᇄശᎌЫྥޟШၶ ശᎌלޑ୤ኵ ଔۖלޑ୤ኵ

Ⴑก঄ ᄂᡛ঄

೩ۡЫྥ B1C3D3E3 B3C1D2E1 B3C1D2E1

ҁ֯঄(N) 542.227 314.793 S/N Ш(dB) -54.684 -51.329 -49.963

S/N Ш׽๡঄ɶ4.721(dB)

Ԓ࢐ԙҳޟȇᡗณΰक़৷ө༊ُڷᏲُ࣏ኇ៪ϸࠈΨσω Ϟᡗ๿Ӱυޟ௰፣࢐ғጂޟȄԪѴȂषоശᎌЫྥࣺၶܻ

ଔۖЫྥޟ׽๡แ࡙ՄِȂϸࠈΨҥ 542N ६࣏ 315NȂࣺ

࿋ܻ 42%ޟή६ൽ࡙ȂਝݎζΪϷџᢎȄ

ѪΙএࠢ፴੫ܒ࣏ёώ७ޟߒ७ಗ࡙Ȃڏ୤ኵ೩ॎһ

࣏ఖω੫ܒȂߒΤ࣏ߒ७ಗ࡙ᄂᡛኵᐃޟҁ֯঄Ȃᡐ౴ኵ Ѕ S/N ШȄҥߒΞӰυਝݎӱᔖߒџޣߒ७ಗ࡙࣏ശωϞ ശᎌЫྥಢӫ࣏ B3C3D2E2Ȃ։৷ө༊ُ 6 ^o ȃ໅ө༊ُ-6 ^o ȃ Ᏺُ 15 ^o ЅΦቅј৷ 0.8mmȄᡐ౴ኵϷݙޟ๖ݎԃߒΪܚ ҰȂषо F ঄σघ࣏ 2-4 ޟ኿ྥپࣼ[11]ࠌџ஠৷ө༊ُȃ

໅ө༊ُЅΦቅј৷Ӗ࣏ኇ៪ߒ७ಗ࡙ޟᡗ๿ӰυȂငҥ ശᎌనӇή໌՗ϸࠈᄂᡛ໔ڥߒ७ಗ࡙σωณࡣШၶᄂᡛ

঄ᇄႱก঄ޟ S/N ШȂԃߒΪΙܚҰȂ๖ݎᡗҰᄂᡛ঄ޟ S/N Ш࣏ 14.894 dB ᇄႱก঄ 12.437 dB ڍޱࣺ৯ϚσȄष оശᎌЫྥࣺၶܻଔۖЫྥޟ׽๡แ࡙ՄِȂߒ७ಗ࡙ҥ 0.53 µm ६࣏ 0.18µmȂή६ൽ࡙ႀ 60% оΰȂ׽๡ਝݎࣥ

࣏݂ᡗȄณՄߒΪϛᇲ৯ޟଓᝦ࡙࣏ 36.9%ȂШ৷ө༊ُȃ

໅ө༊ُЅΦቅј৷ޟଓᝦ࡙݂ᡗଽю೨ӻȂငրᘞԪΝ ӰᄂᡛనӇϛ໌๝໔Ȟ0.1mm/toothȟωܻΦቅј৷оमᡗ

๿Ӱυޟᡗ๿ܒٮϚΪϷ݂ᡗȄ

ω ϛ σ

0 -11 0.5

1

-8 -6 -4 -2 0 2 4 6 8 11

ϛ σ

ω

0 0.5

1

-55 -54 -53 -52 -51 -50 -49 ߒΤ! ಗ࡙ޟ S/N Ш

ᄂᡛጡဴ ҁ֯঄(µm) ᡐ౴ኵ S/N (dB) 1 3.16 0.003 -10.004 2 0.53 0.000 5.565 3 0.53 0.002 5.546 4 1.10 0.001 -0.856 5 1.36 0.000 -2.650 6 1.12 0.007 -0.975 7 0.64 0.013 3.827 8 0.70 0.003 3.119 9 0.37 0.002 8.508 10 0.66 0.049 3.333 11 1.24 0.002 -1.872 12 0.46 0.001 6.674 13 0.60 0.002 4.422 14 0.71 0.007 2.897 15 0.32 0.001 9.789 16 0.29 0.005 10.682 17 0.37 0.006 8.443 18 0.31 0.004 9.867

ߒΞ! ಗ࡙ޟ S/N Шӱᔖߒ ಒဴ לޑ୤ኵ S/N Шҁ֯঄ (dB)

Level 1 Level 2 Level 3 Max-Min B ৷ө༊ُ 1.540 2.104 7.408 5.868 C ໅ө༊ُ 1.901 2.583 6.568 4.667 D Ᏺ! ! ُ 2.335 4.617 4.100 2.282 E Φቅј৷ 0.623 5.829 4.600 5.206

S/N Шᖂҁ֯঄ɶ3.684 (dB)

2.ᚖ१ࠢ፴੫ܒȞӣਢՃኌϸࠈΨЅߒ७ಗ࡙ȟ ҏ؏᡽࢐ᙤҥ዁ጙПݲޟ௰౩ӣਢװϸࠈΨЅߒ७ಗ

࡙ڍএࠢ፴੫ܒઽΣՃ໔оؑڥџ௡ӰυޟശᎌЫྥಢ ӫȄПݲΰ࢐஠ࠉक़ϞϸࠈΨᇄߒ७ಗ࡙ڍএࠢ፴੫ܒޟ S/N Шհ࣏዁ጙ௰፣ݲࠌޟᒯΣᡐኵȂᒯюᡐኵࠌ࢐ӻ१

ࠢ፴੫ܒϞᒋ໔ࡾ኿ȞMPCIȟȄҏМ௴Ңఘלᘪ឴ڒኵ໌

՗ᒯΣᡐኵϞ዁ጙϷസȂϷտᄇϸࠈΨЅߒ७ಗ࡙ۡဎ ωȃϛȃσέএ้઻ԃყ 5ȃყ 6 ܚҰȄҏᄂᡛՃኌϸࠈ ΨЅߒ७ಗ࡙ڍএࠢ፴੫ܒޟ१ौแ࡙ࣺӣȂ࢈џڙۡߒ ΪΠϞ዁ጙೣࠌȂߒϱӓԤ 9 నೣࠌȂᒯюᡐኵһᒵᐅఘ לᘪ឴ڒኵȂӓۡဎϤএ้઻ȂϷտ࣏ߨலωȃωȃϛȃ σȃߨலσȂԃყ 7 ܚҰȄߒΪΠϞ዁ጙೣࠌߒџоߒҰ ԃήȓ

R ₁ ȓif inp1 is σ and inp2 is σ then Rult is ߨலσ R ₂ ȓif inp1 is σ and inp2 is ϛ then Rult is σ

R ₉ ȓif inp1 is ω and inp2 is ω then Rult is ߨலω

ߒΪ! ಗ࡙Ϟ S/N Шޟᡐ౴ኵϷݙ

ಒဴ לޑ୤ኵ Ռҥ࡙ ҁПڷ ֯Пڷ F ঄ ! ଓᝦ࡙(%) B ৷ө༊ُ 2 125.735 62.867 3.133 25.732 C ໅ө༊ُ 2 76.258 38.129 1.900 15.607 D Ᏺ! ! ُ 2 17.190 8.595 0.428 3.518 E Φቅј৷ 2 88.848 44.424 2.214 18.183 ᇲ৯ 9 180.600 20.067 0.000 36.960 ᖂڷ 17 488.631 100

ߒΪΙ! ಗ࡙ϞଔۖЫྥᇄശᎌЫྥޟШၶ ശᎌלޑ୤ኵ ଔۖלޑ୤ኵ

Ⴑก঄ ᄂᡛ঄

೩ۡЫྥ B1C3D3E3 B3C1D2E1 B3C1D2E1

ҁ֯঄(N) 0.53 0.18

S/N Ш(dB) 5.546 12.437 14.895 S/N Ш׽๡঄ɶ9.381(dB)

ߒΪΠ! ዁ጙೣࠌߒ

ߒ७ಗᕹ࡙Ϟ S/N Ш ӻ१ࠢ፴੫ܒϞᒋ໔ࡾ኿

(MPCI) ω ϛ σ ϸ ࠈ Ψ

Ϟ S/N Ш ω ߨலω ω ϛ ϛ ω ϛ σ σ ϛ σ ߨலσ

ყ 5! ϸࠈΨϞ S/N Шޟᘪ឴ڒኵ

ყ 6! ߒ७ಗ࡙Ϟ S/N Шޟᘪ឴ڒኵ

ߨலω ω ϛ σ ߨலσ

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0 1

0 0.5

1

ߒΪέ! ӻ१ࠢ፴੫ܒᒋ໔ࡾ኿Ϟኵᐃ ᄂᡛጡဴ ӻ१ࠢ፴੫ܒϞᒋ໔ࡾ኿

1 0.196 2 0.580 3 0.379 4 0.374 5 0.425 6 0.286 7 0.690 8 0.432 9 0.702 10 0.348 11 0.275 12 0.483 13 0.540 14 0.407 15 0.661 16 0.645 17 0.665 18 0.749

ߒΪѲ! ӻ१ࠢ፴੫ܒϞᒋ໔ࡾ኿(MPCI)ӱᔖߒ ಒဴ לޑ୤ኵ ӻ१ࠢ፴੫ܒϞᒋ໔ࡾ኿(MPCI)

Level 1 Level 2 Level 3 Max-Min B ৷ө༊ُ 0.377 0.449 0.647 0.270 C ໅ө༊ُ 0.465 0.464 0.543 0.079 D Ᏺ! ! ُ 0.479 0.578 0.416 0.162 E Φቅј৷ 0.434 0.529 0.510 0.095

MPCI ޟᖂҁ֯঄ɶ0.491 (db)

ყ 7! ӻ१ࠢ፴੫ܒϞᒋ໔ࡾ኿ȞMPCIȟ

ڏϛ R i ࣏ޟ಑ i న዁ጙೣࠌ inp1 ࣏ϸࠈΨޟ S/N Ш inp2 ࣏ߒ७ಗ࡙ޟ S/N Ш

Rult ࣏ӻ१ࠢ፴੫ܒᒋ໔ࡾ኿ȞMPCIȟ

዁ጙ௰፣Пݲ߽௴Ң[ᡒᒮᑖ-ᡒᒮᑖ-ᡒᒮڷ]ݲȂ၌዁

ጙϽޟПݲࠌٺҢ१ЖݲȂ௰፣๖ݎԃߒΪέȄ஠Ԫ๖ݎ ᇧԙߒΪѲϞӻ१ࠢ፴੫ܒᒋ໔ࡾ኿ȞMPCIȟӱᔖߒȂڏ

ߒΪϤ! ӻ१ࠢ፴੫ܒϞᒋ໔ࡾ኿(MPCI)Ϟᡐ౴ኵϷݙ ಒဴ לޑ୤ኵ Ռҥ࡙ ҁПڷ ֯Пڷ F ঄! ଓᝦ౥(%) B ৷ө༊ُ 2 0.235 0.118 9.501 48.824 C ໅ө༊ُ 2 0.025 0.012 1.000 5.139 D Ᏺ! ! ُ 2 0.080 0.040 3.229 16.595 E Φቅј৷ 2 0.030 0.015 1.230 6.319 ᇲ! ! ৯ 9 0.111 0.012 0.000 23.124 ᖂ! ! ڷ 17 100

ߒΪϲ! ଔۖЫྥᇄӻ१ࠢ፴੫ܒശᎌЫྥಢӫϞШၶ ശᎌלޑ୤ኵ ಒ! ! ဴ ଔۖלޑ୤ኵ

Ⴑก঄ ᄂᡛ঄

Ы! ! ྥ B1C3D3E3 B3C3D2E2 B3C3D2E2

ҁ֯ϸࠈΨ(N) 542.227 397.250 (-54.684dB) (-51.981dB)

ಗ࡙(µm) 0.530 0.180 (5.514dB) (14.894dB) MPCI 0.379 0.734 0.750

ӻ१ࠢ፴੫ܒᒋ໔ࡾ኿(MPCI)Ϟ׽๡ɶ0.371

঄ཕσфߒ౰ࠢࠢ፴ཬѶཕωȄҥ၎ߒџี౪ B3C3D2E2 Ϟ S/N ШശσȂ࢈࣏ശᎌЫྥಢӫȂԪᇄࠉक़൐ᐿՃኌߒ ७ಗ࡙ਢϞശᎌЫྥಢӫࣺӣȄӻ१ࠢ፴੫ܒᒋ໔ࡾ኿

ȞMPCIȟϞᡐ౴ኵϷݙӖܻߒΪϤȂڏϛ৷ө༊ُޟ F

঄࣏ 9.501ȂᏲُޟ F ঄࣏ 3.229Ȃ࢈џրᘞ৷ө༊ُЅᏲ

ُ࣏ӣਢኇ៪ϸࠈΨᇄߒ७ಗ࡙ڍᆍࠢ፴੫ܒޟᡗ๿Ӱ υȂӰԪӵհശᎌЫྥήϞ MPCI ޟեॎਢ໸ՃኌԪڍӰ υޟਝᔖȂႱก๖ݎԃߒΪϲϛܚҰ࣏ 0.734ȂՄٷԪശᎌ Ыྥಢӫ໌՗ᡛᜌᄂᡛܚுϞϸࠈΨ࣏ 397.25NȂߒ७ಗ

࡙࣏ 0.18µmȂࣺᄇᔖϞ MPCI ঄࣏ 0.750Ȃڍޱࣺ৯༉

0.016dB ȂԪ๖ݎᜌ݂ҏᄂᡛϞёݲ዁ԒԙҳȄԪѴȂߒΪ ϲһџࣼюٷӻ१ࠢ፴੫ܒശᎌЫྥಢӫ໌՗ᡛມᄂᡛޟ ๖ݎᄇܻଔۖלޑ୤ኵಢӫϞ S/N Ш׽๡໔ȂڏϛϸࠈΨ घ෵Ѝ 26.7%ࣺ࿋ܻ 2.7dBȇӣਢߒ७ಗ࡙ޟ׽๡ႀ 65.8%

ࣺ࿋ܻ 9.38dBȂਝݎሳ࣏ᡗ๿Ȅ

Ϥȃ๖! ፣

७ሣΦඁդלޑѲএᒵۡޟџ௡Ӱυϛᡗ๿ኇ៪ϸࠈ Ψσωޱٷו࣏৷ө༊ُڷᏲُȂᎌ࿋௡ڙԪΠޱџԤਝ ६ճϸࠈΨඪЀϸࠈᛧۡܒȄՄᄇߒ७ಗ࡙ኇ៪ᡗ๿ޟӰ υٷו࣏৷ө༊ُȃΦቅј৷ڷ໅ө༊ُȄ࿋оϸࠈΨڷ ߒ७ಗ࡙ڍᆍࠢ፴੫ܒΙଔຟեϸࠈࠢ፴ਢȂ৷ө༊ُࠌ

࣏ኇ៪ޟᡗ๿ӰυȄᆣӫоΰӨ໶๖ݎپ௰፣Ȃ৷ө༊ُ

ᄂ࣏এտܖӣਢኇ៪ϸࠈΨᇄߒ७ಗ࡙ޟശ१ौӰυȂ௰

ـڏনӰᔖ࣏७ሣΦϸλ௴ғ৷ө༊ُޟ೩ॎٺλοᎠ

ցȂϸৣಋଶЅ௶юഅԙޟߢתωٺுߒ७ಗ࡙ζᓍϞ෵

ωȄӰԪ७ሣΦඁդלޑޟ೩ॎӵϚཬЅΦλ஼࡙ޟࠉඪ ήᡱ৷ө༊ُ௴ғُ೩ॎᔖԤօܻӣਢᅖٗΰक़ڍᆍࠢ፴ ੫ܒޟሯؑȄ

ҏंـ࡚ҳ७ሣΦڎඁդלޑᄇϸࠈΨڷߒ७ಗ࡙ڍ ᆍࠢ፴੫ܒޟ໔ϽၥਟȂଶџհ࣏७ሣΦڎלޑശٹϽ೩

ॎਢޟ୤ՃϞѴ஠پџװጒ൜ᘗЅϸࠈనӇޟଆ፣Ȃ෈૖

ඪټ७ሣΦڎ݂ጂׇᐌޟ೩ॎПөȄ

ᇬ! ᗂ

ҏंـཐᗂ୽ऋོӵငາΰޟ၄օȂॎหጡဴ࣏ NSC 89-2212-E-262-002 Ȃٺҏंـுоᄂ౪ȄԪѴཐᗂ৿ৱ ᇃ ᢊऋ׬σᏰᐠడف বҗཱིఀ௲ӵ౩፣ᇄᄂᡛП७ޟࡾᏲ ٺҏंـுо໷ցׇԙȄӣਢȂंـҡ೅ρߧӑҡӵᄂᡛ ΰޟڞօȂӵԪΙځमᗂȄ

୤ՃМᝦ

1. Martellotti, M. E., “An Analysis of the Milling Process,”

Trans. ASME, Vol. 63, pp.667 (1941).

2. Koenigsberger, F., and Sabberwal, A. J. P., “Chip Section and Cutting Force during the Milling Operation,” Annals of the CIRP, (1960).

3. Koenigsberger, F., and Sabberwal, A. J. P., “An Investiga- tion into the Cutting Force Pulsation during Milling Op- erations,” International Journal of Machine Tool Design Research, Vol. 1, pp.15 (1961).

4. Fu, H. J., Devor, R. E., and Kapoor, S. G., “A Mechanistic

Model for the Prediction of the Force System in Face- Milling Operation,” Trans. ASME, Vol. 106, pp.81 (1984).

5. Shaw, M. C., Metal Cutting Principles, Clarendon press.

Oxford, (1984).

6. Young, H. T., “Application of Predictive Machining The- ory to More Complicated Process Including Single-Point Oblique Cutting Tools with Other than Single Straight Cutting Edges and Milling, and Experimental Verifica- tion,” Ph.D. Thesis, University of New South Walse, Aus- tralia, (1986).

7. Taguchi, G., Introduction to Quality Engineering, Asian Productivity Organization, Tokyo, (1990).

8. Tarng, Y. S., Yang, W. H., and Juang, S. C., “The Use of Fuzzy Logics in the Taguchi Method for the Optimization of the Submerged Arc Welding Process,” International Journal of Advanced Manufacturing Technology, Vol. 16, pp.688 (1999).

9. Wang, J., and Mathew, P., “Development of a General Tool Model for Turing Operations Based on a Variable Flow Stress Theory,” International Journal of Machine Tools and Manufacture, Vol. 35, No. 1, pp.71 (1995).

10. Phadke, M. S., Quality Engineering Using Robust Design, Prentice Hall, New Jersey, (1989).

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