Transcription

1 Ttle Stud on Estmaton of Thee-Dmens leances Based on Vtual Machnng S oton Devatons uthos Thasana, Woj Edtos Ctaton Issue Date 5- URL Rghts

2 Stud on Estmaton of Thee-Dmensonal Suface Roughness and Toleances Based on Vtual Machnng Sstems Consdeng Knematc Moton Devatons Woj Thasana Febua 5 Doctoal Thess at Osaka Pefectue Unvest

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4 cknowledgment I would fst lke to epess m sncee gattude to Pofesso D. Nobuho Sugmua of the Depatment of Mechancal Engneeng at Poducton Engneeng Laboato, Osaka Pefectue Unvest. He has gven me nvaluable suggestons, futful nstuctons and stong encouagement thoughout the whole wok enablng me to complete m eseach to a successful concluson. He gave me the feedom to lean fom mstakes, and he gentl oblged me to pou the esults n papes and nto a PhD. dssetaton I am also gateful to Pofesso D. Koj Mmua and Pofesso D. Yoshho Ootao of the Depatment of Mechancal Engneeng, Osaka Pefectue Unvest fo beng eamnes fo m fnal pesentaton. I am also thankful to ssocate Pofesso D. Koj Iwamua and ssocate Pofesso D. Yoshtaka Tanmu of the Depatment of Mechancal Engneeng, Osaka Pefectue Unvest fo the valuable suppot and help to ncease the qualt and the geneal compehensblt of m eseach. I would lke to epess m specal appecaton fo the nspaton and assstance of ssocate Pofesso D. Koj Iwamua fo waml suppotng and encouagng me n m laboato lfe. I would lke to thank M. ata Yoshda and M. tsush Takahash who ae/wee n Pofesso D. Nobuho Sugmua Poducton Engneeng Laboato whose suppot and assstance made ths eseach successful. I would also lke to thank M. Njål Vgesdal and D. Rajesh Shestha fo helpng me to check the Englsh gamma of m dssetaton. I would lke to etend m sncee gattude to Tha-Nch Insttute of Technolog and Osaka Pefectue Unvest fo suppotng me wth the scholashp, accommodaton and gvng me the oppotunt to stud fo the doctoal degee. Fnall, I would lke to thank m mothe, m wfe and sblngs fo keepng me awae of the dffeence between lfe and wok dung the last.5 eas. Now, m PhD havng been fnshed, I feel eleved and nclude all m well-wshes n m thanks fo the contnuous encouagement fo ths eseach.

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6 Table of Contents Lst of Fgues... Lst of Tables... v v. Intoducton. Peface.... Backgound....3 Objectves of the Reseach Oganaton of the Dssetaton Revew of Relevant Lteatues. Knematc moton devatons.... Vtual Machnng Bong pocess modelng Tunng pocess modelng Thee-Dmensonal Suface Roughness Thee-Dmensonal Toleances Smulaton of Vtual Machnng Sstems n Bong and Tunng Pocesses 3. Intoducton Modelng of Shape Geneaton Motons Homogeneous pont of coodnates Tansfomaton of coodnates Homogeneous tansfomaton mat of otatonal and tanslatonal eos Machne Tool Coodnate Sstem, Poston and Oentaton Eos Machne tool coodnate sstem of bong pocesses Machne tool coodnate sstem of tunng pocesses Knematc Moton Devatons n Bong Pocesses Shape geneaton motons n bong pocesses Fomulaton of knematc motons n bong pocesses... 4

7 3.4.. Spndle moton Bong ba moton Tool tp moton Fomulaton of knematc motons of cuttng edge n bong pocesses Knematc Moton Devatons n Tunng Pocesses Shape geneaton motons n tunng pocesses Fomulaton of knematc motons n tunng pocesses Spndle moton Caages moton Coss sldes moton Tool tps moton Fomulaton of knematc motons of cuttng edge n tunng pocesses Vtual Machnng Sstems Vtual machnng sstems fo bong and tunng pocesses Smulaton of 3-dmensonal boed and tuned faces Smulaton of boed and tuned faces wthout knematc devatons Smulaton of boed and tuned faces wth knematc devatons Concluson Estmaton of 3-Dmensonal Suface Roughness Includng Knematc Moton Devatons 4. Intoducton Refeence Datum fo Clnde ssessment Mathematcal Models of Least Mean Squaes Devaton of least mean squaes lgothm fo calculatng paametes Fomulaton fo Estmaton of the Suface Roughness Two-dmensonal suface oughness Theoetcal suface oughness Mamum heght of the assessed pofle thmetcal mean devaton of the assessed pofle... 7

8 Root mean squae of the assessed pofle Thee-dmensonal suface oughness Samplng aea Mamum heght of the Suface thmetc mean and oot mean squae heght of the suface Case Stud Estmaton of boed and tuned faces wthout knematc devatons Estmaton of boed and tuned faces wth knematc devatons Concluson Estmaton of 3-Dmensonal Toleances Includng Knematc Moton Devatons 5. Intoducton Geometc Toleances and Devatons of Featues Featues fo geometc toleances Toleance ones and devaton paametes Statstcal popetes of devaton paametes Dstbuton of devaton paametes Estmaton of standad devatons Knematc Motons Devatons of Lnea Tables and Rota Tables Based on Geometc Toleances Geometc devatons of components and knematc moton devatons of machne tools Geometc Devaton of lnea and ota tables Modelng of knematc moton devatons of lnea tables Modelng of knematc moton devatons of ota tables nalss of Knematc Moton Devatons of Rota Tables nalss of Knematc Moton Devatons of Fve-s Machnng Centes Modelng of knematc motons nalss of knematc moton devatons of fve-as machnng centes Estmaton of 3D Toleances Based on Smulaton of Vtual Machnng Includng Knematc Moton Devatons... 7

9 5.6. Vefcaton of 3-dmensonal toleances Case stud Estmaton of boed and tuned faces wthout knematc devatons Estmaton of boed and tuned faces wth knematc devatons Concluson Conclusons 6. Conclusons... 6 Refeences... 9 Lst of Publcatons v

10 Lst of Fgues Fg. - Dssetaton chaptes and the elatonshp... 7 Fg. - Ovevew of the eo budget n a machne tool and the factos affectng t... Fg. - chtectue of a vtual machnng sstem... 4 Fg. 3- Ke components of the vtual machnng sstem... 6 Fg. 3- Factos affectng machnng eos... 7 Fg. 3-3 Mathematcal model of machne tool... 8 Fg. 3-4 Chan-lnk dagam epesentng the shape geneaton motons... 8 Fg. 3-5 Lnea moton caage n Y-as... 3 Fg. 3-6 S eos of sngle as lnea moton Fg. 3-7 Coodnate sstems fo bong pocesses Fg. 3-8 Stuctues and coodnate sstems fo tunng pocesses Fg. 3-9 Coodnate sstems and the devatons of bong pocesses Fg. 3- Cuttng efeence ponts on dffeent nsets... 4 Fg. 3- Tool tps and cuttng edges of bong pocesses... 4 Fg. 3- Coodnate sstems and the devatons of tunng pocesses Fg. 3-3 Tool tps and cuttng edges of tunng pocesses Fg. 3-4 Flow chat fo smulatons of the bong and tunng pocesses... 5 Fg. 3-5 Detemnaton of goove se fomed b tool nose geomet wth knematc devatons 5 Fg. 3-6 Estmated geometes of boed faces wthout knematc moton devatons Fg. 3-7 Estmated geometes of tuned faces wthout knematc moton devatons Fg. 3-8 Estmated geometes of boed faces wth knematc moton devatons Fg. 3-9 Estmated geometes of boed faces wth knematc moton devatons Fg. 4- Ke components of estmaton of the 3D suface oughness... 6 Fg. 4- Coodnate sstem fo measung devatons... 6 Fg. 4-3 Flowchat fo calculatng paametes of least mean squaes Fg. 4-4 Suface oughness temnolog Fg. 4-5 Idealed model of D suface oughness... 7 Fg. 4-6 Defnton of the R ampltude paametes... 7 Fg. 4-7 Defnton of the Ra ampltude paametes... 7 v

11 Fg. 4-8 Coodnates used fo measuement of suface oughness... 7 Fg. 4-9 Defnton of S of the suface Fg. 4- D oughness pofle s evaluated b measung the lnes fo boed faces Fg. 4-3D suface oughness s evaluated b measung the aeas fo boed faces Fg. 4- D oughness pofle s evaluated b measung the lnes fo tuned faces Fg D suface oughness s evaluated b measung the aeas fo tuned faces Fg. 5- Ke components of estmaton of the 3D toleances on the vtual pats Fg. 5- Defnton of featues Fg. 5-3 Tpes of toleance ones Fg. 5-4 Defnton of geometc toleance of plane featues Fg. 5-5 Defnton of geometc toleance of as featues Fg. 5-6 Relatonshps between knematc moton devatons and devatons of components... 9 Fg. 5-7 Lnea and ota tables and the connectng elatonshps... 9 Fg. 5-8 Featues connectng a pa of unt Fg. 5-9 Hoontal ota tables -as table and the gude-was Fg. 5- Two-as ota tables Fg. 5- Mean values and standad devatons of knematc moton of pont P Fg. 5- Fve-as machnng centes... Fg. 5-3 Ses and stokes of lnea and ota tables... Fg. 5-4 nalss esults of tpe machnng cente... 5 Fg. 5-5 nalss esults of tpe machnng cente... 6 Fg. 5-6 nalss esults of tpe 3 machnng cente... 7 Fg. 5-7 Coodnate sstem fo measung devatons... 8 v

12 Lst of Tables Table 3- Tansfomaton matces descbng tanslaton motons and ota moton... 3 Table 4- Estmated D and 3D suface oughness of bong and tunng pocess smulatons wthout knematc devatons Table 4- Estmated D and 3D suface oughness of bong pocess smulatons wth knematc devatons Table 4-3 Estmated D and 3D suface oughness of tunng pocess smulatons wth knematc devatons Table 5- Geometc toleances and the toleance ones Table 5- Devaton paametes of toleance featues Table 5-3 Dstances between a pa of connectng tables... Table 5-4 Dstances between a pa of connectng tables... Table 5-5 Ses of ota tables fo tpes, and 3... Table 5-6 Table postons to be set n analss... Table 5-7 Estmated 3D toleances of bong and tunng pocess smulatons wthout knematc devatons... Table 5-8 Estmated suface oughness and clndct n bong pocess smulatons wth knematc moton devatons... Table 5-9 Estmated suface oughness and clndct n tunng pocess smulatons wth knematc moton devatons... v

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14 Chapte Intoducton - -

15 . Intoducton. Peface In the most ecent decade, evolutons n the machne ndustes ae constantl eplong sstems and methods to ncease the qualt and the elablt of the poducts and to decease the costs of the machnng opeatons. Nowadas, the poposed machnng pocesses contan collaboaton wth advances n dgtal engneeng technologes. CD/CE/CM sstems ae now beng wdel appled to desgn, analss and manufactung pocesses of mechancal poducts. Vtual manufactung smulaton s a dgtal engneeng technolog whch can pove an mpotant tool to educe the developmental costs and the tme equed fo phscal pototpng n ode to estmate machnng accuac, suface oughness and the geometc dmensonng and toleancng whch s one of the most mpotant chaactestcs of the Compute Numecal Contol CNC machne tools fo geneatng the poducts wth hgh accuac and complcated geometes. The eseach summaed n ths doctoal dssetaton deals wth a smulaton based estmaton of 3-dmensonal 3D suface oughness and toleances ncludng knematc moton devatons. Ths dssetaton pesents the basc concepts and stud of vtual machnng of bong and tunng pocesses, the estmaton of the 3D suface oughness and the 3D toleances, based on geometc toleances and the knematc moton devatons of the CNC machnng centes and CNC tunng centes.. Backgound The accuac of a machne tool affects the qualt of fnshed poducts and also the ablt fo economc poducton. Nowadas, the needs fo pecson machnng ae manl dven b ICtechnolog, lqud cstal dspla, and plasma dspla. Snce the ntegated ccut was nvented, n 958, the need to ncease the numbe of tansstos on a sngle chp has been gowng hghe and hghe. Man actvtes n the ndust and academa have been amed at nceasng the pecson of postonng and machnng to ceate hgh pecson poducts and pocesses. Manufactung fo pecse poducts concens hgh accuac n se, shape and suface qualt. To acheve a hgh accuac, cetan factos have to be undestood fom the desgn to the manufactung pocess, such as nteacton between tools and wokpeces, behavos of machne tools unde themal, dnamc and knematc loadng. The qualt of the fnshed poducts s lagel nfluenced b the followng factos: Devatons fom the planned elatve movement between the tools o tool caes and the wokpeces o wokpece suppots. Wea condtons and elastc defomatons of the tools. Elastc defomatons of the wokpeces and clampng elements. - -

16 The devatons fom the defned elatve motons between the tools and wokpeces ma be gouped nto geometc and knematc categoes. The geometc devaton conssts of postonal naccuaces and eos n the shape of machne components tables, tool holdes, gudes, etc.. The knematc devaton occus n coodnate movements,.e. functon movements thead cuttng, gude-wa contol etc.. These eos ae tansmtted nto the accuac of the wokpeces n vang amounts, dependng on the patcula poducton condtons, whch appl n the gven case. Both tpes of devatons ae the esults of poducton and assembl eos n the elements whch ae used n the machne constucton Nedno, 999. Vaous tpes of CNC machne tools ae now beng desgned and appled to machnng pocesses of complcated machne poducts. The machnng accuac s one of the most mpotant chaactestcs of the CNC machne tools fo geneatng poducts wth hgh accuac and complcated geometes. Some eseachs have been caed out to anale the machnng accuac of the machne tools based on the devatons of the shape geneaton motons between the tools and the wokpeces Sugmua, et al., 98; Reshetov, et al., 988; Sakamoto, et al., 994; Sugmua, et al., 998. Howeve, the knematc moton devatons of the machne tools ae stongl nfluenced b the geometc devatons of the components, such as gude was and beangs. Theefoe, t s now equed to claf the elatonshps between the knematc moton devatons of the machne tools and the geometc devatons of the components, fom the vewponts of the desgn and the manufactung of the machne tools and the components. Wth egad to the geometc devatons of the machne components, much eseach wok has been caed out to deal wth the dmensonal toleances and the geometc toleances, amed at ealng sstematc analss and desgn methodologes fo the thee dmensonal machne poducts Ro, et al., 99; Voelcke, 993; Ngam and Tune, 995; Ngo, et al.,. Howeve, the elatonshps between the knematc moton devatons and the geometc devatons of the components have not et been clafed, as the lnea and ota tables of the machne tools ae suppoted b moe than two-gude was and that all the geometc devatons of ndvdual gude was affect the knematc moton devatons of the lnea and ota tables. Machnng pocesses on the CNC machne tools fo geneatng poducts wth hgh accuac and complcated geometes ae nheentl comple, and lead to use empcal methods fo pocess developments. In patcula, pocess paametes such as machnng speeds, feed ates and toolng ae usuall selected based on handbooks and tal-and-eo pototpng. Howeve, these methods do not guaantee the pocess paametes whch satsf the equed qualt Ramaswam,. Snce the eal 99s, a paadgm shft n manufactung fom eal to vtual poducton has esulted n a buld-up of eseach nteests n the smulaton technques. Wth the ad of computes, t becomes possble to smulate some of the actvtes of phscal manufactung sstems. The man objectve of the vtual poductons s to undestand and to emulate the - 3 -

17 behavo of the manufactung sstems on the computes po to the phscal poductons, amng at educng the amount of testng and epements on the shop floos. The ae theefoe called vtual manufactung, vtual machne tools, vtual machnng, vtual assembl, vtual toolng and vtual pototpng bdul Kad, et al.,. Some smulaton models fo the machnng pocesses have ecentl been poposed to pedct the dmensons, geometes and geometc devatons of the machned pats, amng at nvestgatng the sutable machnng pocess paametes Govk, et al., ; Luo, et al.,. Howeve, the poposed models have been appled onl to the lmted aeas of the machnng pocesses and have not et consdeed the vefcaton of the geneated faces of bong and tunng pocesses ncludng knematc moton devatons. Once the pats ae machned on CNC machne tools, the suface oughness and geometc dmensonng and toleancng need to be nspected to ensue complance wth the desgn specfcatons. Wth nceasng focus on pecson manufactung ndustes, especall n the automotve, electonc, defense and aeospace sectos, % nspecton of pats s mandated to ensue poduct elablt and functonng Ramaswam,. Theefoe, the poposed model fo the estmaton of the suface oughness and the geometc dmensonng and toleancng have been appled to the vtual machnng smulatons whch can estmate and mpove the machnng pocesses befoe eal machned pats. The smulaton sstems have become an mpotant tool to educe the development cost and tme equed fo phscal pototpng, the poduct desgn and the pocess plannng fo select the machnng pocess paametes. It can also educe the lead tme to maket, and mpove the esponsveness and compettveness of the manufactues. It s essental to establsh effectve and effcent estmaton methods of the suface oughness and the geometc dmensons and toleances fo the ndustal poducts such as automotve, electoncs and aeospace pats, n ode to meet the keen competton of the global econom..3 Objectves of the Reseach Suface oughness and toleances ae mpotant n poduct desgn and manufactung, whch deal wth checkng the feasblt and qualt of ndvdual pats and assembl pats, because t affects not onl the pefomance of the poducts, but also the costs. To facltate the pedcton and adaptaton of machned pats n CNC machne tools, a new appopate methodolog s needed to poduce and to estmate the suface oughness and toleances befoe the eal and phscal machnng pocesses. Ths wll facltate the adaptaton to changes n the machne ndustes, n ode to ncease the qualt and elablt of the poducts and educe the costs of the machnng pocesses. The vtual machnng appoaches ae becomng nceasngl mpotant fo estmaton of 3D suface oughness and toleances of machnng pocesses ncludng knematc moton devatons. The vtual machnng povdes a sstematc wa to estmate the 3D suface oughness and toleances wth the accuac and the elablt of the poducts and manufactung pocesses

18 Ths eseach apples a vtual machnng model to estmaton of the 3D suface oughness and toleances ncludng knematc moton devatons of bong and tunng pocesses. The objectve of ths eseach s to develop a vtual machnng model fo boed and tuned pats to anale the effect of machnng pocess paametes on the qualt of the fnal poducts. vtual pat pofle can be geneated usng the vtual machnng sstem, based on the desgn specfcatons, machnng pocess paametes, ncludng the knematc moton devatons of the machne tools. The pat pofles ae thus ceated to nvestgate the effects of the machnng paametes along wth the statc eos n the machne beds, spndle eos and tool geometes, and to stud the capablt of the machne tools to poduce pats meetng the desgn equements. The objectves of ths eseach ae lsted as follows; Smulaton of the machnng pocesses ncludng knematc moton devatons The objectve of ths secton eseach s to popose a smulaton model of the machne tools and the machnng pocesses n whch a smulaton model s poposed and appled to the estmaton of vtual machnng n bong and tunng pocesses ncludng knematc moton devatons. set of ponts on the boed and tuned faces ae obtaned though the smulaton. The poposed model epesents the bong and tunng pocesses based on both the shape geneaton motons and the cuttng tool geometes. The ndvdual motons ae mathematcall descbed b 4 b 4 tansfomaton matces ncludng the knematc moton devatons. Emphass s gven to the modelng and analss of the bong and tunng pocesses of the sngle pont tools. Estmaton of the 3D suface oughness ncludng knematc moton devatons The objectve of ths secton eseach s to popose an estmaton of 3D suface oughness based on smulaton of vtual machnng n bong and tunng pocesses ncludng knematc moton devatons on CNC machnng centes and CNC tunng centes, espectvel. smulaton model s poposed to epesent the bong pocess wth knematc moton devatons of the spndles of the mllng machnes, and to epesent the tunng pocess wth knematc moton devatons of the spndles, caages and coss sldes of the tunng machnes. set of ponts on the boed and tuned faces ae obtaned though the smulaton. The poposed model epesents the bong and tunng pocesses based on both the shape geneaton motons and the cuttng tool geometes. The ndvdual motons ae mathematcall descbed b combnng 4 b 4 tansfomaton matces ncludng the knematc moton devatons. Emphass s gven to the modelng and analss of the bong and tunng pocess of the sngle pont tools. sstematc method s also poposed to vef the D and 3D suface oughness of the boed and tuned faces base on the smulaton esults. nalss of the knematc moton devatons of machnng centes and estmaton of the 3D toleances ncludng knematc moton devatons - 5 -

19 The objectve of ths secton eseach s to establsh mathematcal models epesentng the knematc moton devatons of the machnng centes, on the bass of the geometc toleances of the components, and to appl the models to theoetcal analss of both the knematc moton devatons of the machnng centes and the estmaton of 3D toleances. In the pevous papes Satonaka, et al., 7b; Satonaka, et al., 8, a mathematcal model has been poposed to epesent the knematc moton devatons of the lnea tables and the poposed model was appled to the analss of the knematc moton devatons of the lnea tables and the 3-as machnng centes. Howeve, the ota tables have not et been dscussed n detal Watabk, et al., 9. The knematc moton devatons of the machnng centes ae estmated based on the models n the vaous condtons of the geometc toleances of the components and the vaous table postons, to nvestgate the nfluence of the geometc toleances of the components on the knematc moton devatons of the fve-as machnng centes. The developed model of the machne tools ae appled to the estmaton of 3D toleances based on the knematc moton devatons on CNC machnng centes and CNC tunng centes. The smulaton of vtual machnng model s epanded to estmate the 3D toleances both the bong and tunng pocesses wth knematc moton devatons. set of ponts on the boed and tuned faces ae obtaned though the smulaton. The poposed model epesents the bong and tunng pocesses based on both the shape geneaton motons and the cuttng tool geometes. The ndvdual motons ae mathematcall descbed b combnng 4 b 4 tansfomaton matces ncludng the knematc moton devatons. Emphass s gven to the modelng and analss of the bong and tunng pocesses of the sngle pont tools. sstematc method s also poposed to vef the 3D toleances of the boed and tuned faces based on the smulaton esults..4 Oganaton of the Dssetaton The oganaton of the dssetaton chaptes and the elatonshps ae shown n the Fg. -. Chapte povdes a bef ntoducton of the hstocal backgound of the eseach, and clafes the necesst and objectve of the eseach. Chapte evews the backgound and mpotance of the conventonal methods and new appoaches fo analss knematc moton devatons and the geometc devatons, vtual machnng, 3D suface oughness and 3D toleances based on the lteatue suve, new aeas fo eseach ae dentfed and poposed. Chapte 3 dscusses the vtual machnng model epesentng the vtual machnng centes fo the bong pocesses and vtual tunng centes fo the tunng pocesses, whch nclude the knematc moton devatons. The boed and tuned faces geneated ae obtaned as a set of ponts and evaluated to nvestgate the effect of vaous pocess paametes on the geomet of the pats. Once the pat s vefed vtuall, the pefomance of the machnng pocess paametes to - 6 -

20 geneate a pat that meets the equed qualt specfcatons can be nvestgated fo estmaton the 3D suface oughness and toleances based on the smulaton esults. Fg. - Dssetaton chaptes and the elatonshp Chapte 4 dscusses the estmaton of 3D suface oughness of poduced b vtual bong and tunng machnng pocesses. The estmaton of 3D suface oughness estmated both the - dmensonal D and 3D though the bong and tunng pocess smulatons wth knematc moton devatons. model s poposed to epesent the knematc motons of the cuttng edges aganst the wokpeces, takng nto consdeaton the knematc devatons of the machnng centes and the tunng centes. Detals of the vtual machnng module ae poposed to estmate the geometc devatons of the machned face based on the knematc motons of the cuttng edges. poposed model s appled to the smulaton of the smple bong and tunng pocess, - 7 -

21 the geometes of the machned faces ae estmated, based on the cuttng condtons, the tool geometes and the knematc devatons of the bong and tunng pocesses. method s also poposed to estmate both the D and 3D suface oughness based on the bong and tunng pocess smulaton wth the knematc moton devatons. Case studes ae shown wth eamples of the geneated faces b bong and tunng pocess smulatons consdeng knematc devatons n ode to estmate the 3D suface oughness. Chapte 5 dscusses the estmaton of 3D toleances ncludng knematc moton devatons. In the begnnng, a mathematcal model of knematc moton devatons of machne tools s dscussed on the bass of the geometc toleances. The shape geneaton motons ae bases fo analss of machne tools ncludng both the lnea tables and ota tables. The 3D toleances of bong and tunng pocesses ae analsed based on the machne tool models ncludng knematc moton devatons. sstematc method s poposed n ths secton to smulate the shape geneaton pocesses n both the bong and tunng opeatons, to estmate the geometc dmensonng and toleancng of both boed and tuned faces, based on the machnng paametes. The shape geneaton motons wth devatons ae mathematcall descbed b combnng 4 b 4 tansfomaton matces. set of ponts on the boed and tuned faces ae geneated though the smulatons, and an assessment suface s obtaned as the datum efeence to estmate the 3D toleances, based on the ponts geneated b the bong and tunng pocess smulatons. Chapte 6 summaes the doctoal dssetaton

22 Chapte Revew of Relevant Lteatues - 9 -

23 . Revew of Relevant Lteatues The lteatues elated wth smulaton based estmaton of 3-dmensonal suface oughness and toleances ncludng knematc moton devatons ae evewed befl n ths chapte and dscussed below.. Knematc moton devatons Vaous tpes of CNC machne tools ae now beng desgned and used n machnng pocesses geneatng complcated machne poducts. The machnng accuac s one of the most mpotant chaactestcs of these machne tools because the poducts ma have hghl complcated geometes. ccuac can be defned as the degee of ageement o confomance of a fnshed pat wth the equed dmensonal and geometcal accuac Jedejewsk and Modck, 997; Ramesh, et al.,. Eo, on the othe hand, can be undestood as an devaton n the poston of the tool s cuttng edge fom the poston theoetcall equed to poduce a wokpece of the specfed toleance Mos, 997; Ramesh, et al.,. The eos can be classfed nto two categoes namel quas-statc eos and dnamc eos; Quas-statc eos ae devatons between the tool and the wokpece that ae slowl vang wth tme and elated to the stuctue of the machne tool tself. These souces nclude the geometc/knematc eos, eos due to dead weght of the machne s components and eos due to themall nduced stans n the machne tool stuctue. Dnamc eos, on the othe hand, ae caused b souces such as spndle eo moton, vbatons of the machne stuctue, contolle eos etc. These ae moe dependent on the patcula opeatng condtons of the machne. The geometc/knematc devatons ae quas-statc eo souces between the tool and wokpece of machne tool. In geneal machne tools, especall machnng cente and tunng cente consst of a bed, column, spndle and ts slde and the vaous lnea and/o ota aes. Each of these elements contbutes to the total devatons of the sstem that s epesented b the eo budget. Theefoe, eos can boadl be gouped nto thee majo classes namel geometc and knematc eos, tempeatue nduced eos o themal eos and cuttng foces nduced eos. n ovevew of the eo budget of a machne tool and the factos affectng the same s gven n Fg. -. Whle these ae the majo contbutos to the volumetc eo of a machne tool, othe eos also contbute to the oveall eo, though not as sgnfcantl Ramesh, et al.,. - -

24 Fg. - Ovevew of the eo budget n a machne tool and the factos affectng t Ramesh, et al., The geometc/knematc devaton shows as above s the most poblem n the eo budget n a machne tool whch s quas-statc eo souces between the tool and wokpece of machne tool, account fo about 7 pecent of the total eo of the machne tool whch ae a majo focus of eo compensaton eseach Evans, 996; Ramesh, et al.,. Theefoe, n ths eseach focus on the lteatue evew of geometc and knematc eos. Geometc devatons ae eos that ae etant n a machne on account of ts basc desgn, naccuaces bult-n dung assembl and as a esult of the components used n the machne. s such, the fom one of the bggest souces of naccuac. These eos ae concened wth the quas-statc accuac of sufaces movng elatve to one anothe, lke suface staghtness, suface oughness, beang pe-loads etc. Geometc eos have vaous components lke lnea dsplacement eo postonng accuac, staghtness and flatness of movement of the as, spndle nclnaton angle, squaeness eo, backlash eo etc N, 997; Ramesh, et al.,. Knematc devatons ae concened wth the elatve moton eos of seveal movng machne components that need to move n accodance wth pecse functonal equements. These eos ae patculal sgnfcant dung the combned moton of dffeent aes as n the case of gea hobbng o pofle machnng whee co-odnaton of ota wth espect to lnea aes o lnea wth espect to lnea aes s of pme mpotance. Such eos occu dung the eecuton of lnea, ccula o othe tpes of ntepolaton algothms and ae moe ponounced dung actual machnng Ramesh, et al.,. - -

25 The modelng of geometc/knematc eos n machne tools has been epoted fo a couple of decades. Some eseach wok has been caed out fo the nvestgaton of the geometc/knematc devatons modelng of machne tool Sugmua, et al., 98; Kdena and Feea, 994; Potman and Inasak, 996; Sugmua and Muabe, 997; Okafo and Etekn, ; Ramesh, et al., a, b; Bohe, ; Hsu and Wang, 7; Satonaka, et al., 8; Uddn, et al., 9; Ibaak, et al.,. The wok can be dvded nto thee categoes; the fst set of papes manl focuses on developng a model fo geometc/knematc eos and othe eos such as themal, vbaton, and cuttng foces elated eos etc. The second set ncludes eo compensaton algothms also and descbes vaous means to compensate fo eos. The thd set manl focuses on developng of the knematc devatons model of the machne tools based on the shape geneaton motons between the tools and the wokpeces n ode to smulate and estmate n the machnng accuac. Keepng n lne wth the objectves of m cuent eseach, the lteatue evew wll focus on aspects of the knematc devatons model based on the shape geneaton motons between the tools and the wokpeces. Some of the ke papes n the aea of knematc moton devatons based on the shape geneaton motons modelng ae dscussed below. One of the ealest dscussons of the modelng of the shape geneaton motons of machne tool can be found n Sugmua et al. 98. The appoach to the modelng taken b Sugmua et al. 98 s smla to the appoach of Reshetov and Potman 988 and Mowak et al Inasak 994 has poposed a theo of geneaton motons fo machne tools, defned the mathematcal model of a machne tool and the coodnate tansfomaton matces. The shape geneaton moton can be epessed b a chan of elatve motons. Potman and Inasak 996 have poposed a theo of fom-shapng sstems and ts applcaton to gndng machnes whch s smla to appoaches wth shape geneaton motons. The fom-shapng sstem enables the smulaton of the fom-shapng pocess, and takes nto account machne tool eo, facltatng quanttatve nvestgaton of the nfluence of ths eo on the machnng accuac. The compute smulatons and the actual gndng tests eveal the pactcalt of the sstem fo analss of the machnng accuac. Sugmua and Muabe 997 have poposed a stud of analss of algnment eos of 5-as machne tools. The eseach has developed a sstematc desgn method of mult-as machne tools based on a mathematcal model epesentng the shape geneaton pocesses of the machne tools. The model descbes the elatve motons between the tool and the wokpece b combnng 4 b 4 homogeneous tansfomaton matces. Machnng eos of vaous tpes of 5-as machne tools ae nvestgated though smulaton b applng the poposed model, amed at vefng adaptablt of the feed as confguatons of the machne tools fom the vewpont of the machnng eos. Tsutsum and Sato 4 have poposed the dentfcaton of angula postonal devatons nheent to 5-as machnng centes wth a tltng-ota table b smultaneous fou-as contol - -

26 movements. The pape ams to popose a method of estmatng the eght devatons wthn the thteen sstematc devatons n a fve-as machnng cente whch Inasak et al. 997 has ponted out n the shape geneaton theo of machne tools - Its bass and applcatons. The valdt of the poposed method has been confmed b smulaton. Fou of the eght devatons ae dentfed b applng both the measued data b a ball ba and the efeence data calculated fo the smultaneous fou-as contol movement to the obsevaton equaton. The othe fou devatons ae geometcall dentfed. The poposed method s effectve fo dentfng the devatons nheent to fve-as machnng centes. Uddn et al. 9 have poposed the pedcton and compensaton of machnng geometc eos of fve-as machnng centes wth knematc eos. Ths pape pesents a scheme to pedct and evaluate the machnng accuac of a fve-as machnng cente wth ts knematc eos. Thee knematc eos assocated wth lnea aes and eght knematc eos assocated wth ota aes of the machnng cente whch caed out n the shape geneaton theo of machne tools b Inasak et al. 997 ae consdeed and dentfed pactcall b a double ball ba DBB method. B usng an eo model wth the knematc eos, thee-dmensonal ntefeence of the tool and the wokpece s calculated along the tool path to smulate the machnng geometc eo unde the nfluence of the machne s knematc eos Ibaak et al. have poposed machnng tests fo a fve-as machne tool such that ts knematc eos can be sepaatel dentfed b evaluatng the geometc eo of fnshed wokpeces. In each machnng patten, a smple staght sde cuttng usng a staght end mll s pefomed. Epemental esults demonstate that the nfluence of knematc eos can be obseved n a ve compehensve manne on eo pofles of fnshed wokpeces. The machnng tests pesented n ths pape s to dentf eght knematc eos assocated wth ota aes defned n the shape geneaton theo of machne tools Inasak et al. 997 have ponted out. lthough etensve eseach has been conducted to model the effect of knematc moton devatons and anale the machnng accuac of the machne tools based on the devatons of the shape geneaton motons between the tools and the wokpeces. Howeve, the knematc moton devatons of the machne tools ae deepl nfluenced b the geometc devatons of the components, such as gude was and beangs. Theefoe, t s now equed to claf the elatonshps between the knematc moton devatons of the machne tools and the geometc devatons of the components, fom the vewponts of the desgn and the manufactung of the machne tools and the components. In ths eseach, the shape geneaton motons method has been used to model the knematc moton devatons n the machne tool, on the bass of the geometc toleances of the components and vtual machnng n ode to estmate the thee-dmensonal 3D suface oughness and toleances

27 . Vtual Machnng Snce the eal 99s, a paadgm shft n manufactung fom eal to vtual poducton has esulted n a buld-up of eseach nteests n the smulaton technques. Wth the ad of computes, t becomes possble to smulate some of the actvtes of phscal manufactung sstems. The man objectve of the vtual poductons s to undestand and to emulate the behavo of the manufactung sstems on the computes po to the phscal poductons, amng at educng the amount of testng and epements on the shop floos. The ae so called vtual manufactung, vtual machne tools, vtual machnng, vtual assembl, vtual toolng and vtual pototpng bdul Kad, et al.,. Fg. - chtectue of a vtual machnng sstem ltntas, et al., 4 The vtual machnng of pats b consdeng the phscs of the manufactung pocesses has ecentl been evolvng. The vtual machnng concept s llustated n Fg. -. The Compute ded Desgn CD model of the pat s used to geneate Numecal Contol NC pogams n a Compute ded Manufactung CM envonment whee the pocess plannes desgn tool path stateges and select cuttng condtons based on the epeence. The NC pogam s ted on a phscal machne, and f the pocess s found to be fault, the tal and eo ccle between the CM and phscal machnng steps s epeated untl a satsfacto esult s obtaned. The am of the vtual machnng s to educe o even elmnate phscal tals b smulatng the phscal opeatons n dgtal envonments ahead of costl poducton as ntoduced b ltntas n 99 ltntas and Spence, 99; ltntas, et al., 4. Eale eseach n ths aea of vtual machnng s mostl focused on machnng pocesses such as: mllng pocesses, tunng pocesses, gndng pocesses etc. The analss s nvolved n the pocess optmaton, numecal analss and paamete pedcton such as foce estmaton, mateal emoval ate, machnng eo, machnng tme, feed, tempeatue etc. Keepng n lne wth objectves of the pesent eseach, the lteatue evew wll focus on aspects of the vtual machnng on analss of bong and tunng pocesses. Theefoe, seveal eseaches have focused on development of models fo vaous vtual machnng and analss of bong and tunng pocesses ae dscussed below

28 .. Bong pocess modelng Consdeable wok has been epoted on vtual machnng modelng of bong pocesses. The motvaton fo most of ths eseach has been mpoved numecal analss and paamete pedcton such as cuttng foce estmatons, machnng eo, feed, tempeatue etc. Rgal et al. 998 have poposed a model fo smulaton of vbatons dung bong opeatons of comple sufaces. The poposed pocedue ntegates a fnte element method FEM analss and a lnea model of the cuttng pocess based on equvalent cuttng edge geomet. On the bass of a paameteed model of the tool-mateal nteacton, a lnea FEM model descbng the behavou of the wokpece, tool and the contact s pesented. The fequenc esponses ae pocessed and the smulaton etends wth a med pocedue FEM analss and smulaton usng Matlab. Howeve, ths eseach dd not consde the machnng pocess analss and have not et consdeed the vefcaton of the geneated faces. Recentl, some models have been poposed fo both the machne tools and the machnng pocesses and appled to the analss of such chaactestcs as geometc devatons, knematc devatons, and dnamcs of the machne tools, the machnng pocesses and themal epanson n machne tools. Laoglu et al. have poposed dnamcs of bong pocesses: Pat III-tme doman modelng. Ths atcle pesents a mathematcal model and a computatonal algothm fo tme doman model of bong pocess dnamcs. The model was developed n a modula stuctue. It conssts of a wokpece geomet and suface topogaph module, knematcs and tool poston module, dnamc chp load module, dnamc cuttng foce pedcton module and stuctual dnamcs module. The tme doman model takes the cuttng pocess paametes, tool and wokpece geometes and the modal paametes as nputs. It pedcts nstantaneous cuttng foces and vbatons along the machnng tme, and machned wokpece topogaph as outputs. Some of the smulated and epemental esults fo vaous cuttng condtons wee pesented and compaed fo valdaton puposes. The epemental and smulaton esults show good ageement. tabe et al. 3a, 3b have poposed mechancs of bong opeatons. The mechancs model pesented n ths pape s used n pedctng the cuttng foces geneated b nseted bong heads wth unouts and pesented n mult-nset bong heads. Ths atcle pesents a mathematcal model fo the cuttng foce sstems as a functon of tool geomet, chp load, cuttng edge contact length and pocess paametes such as feed ate, cuttng speed, adal depth of cut based on the phscs, knematcs and mechancs of the bong pocess. The model developed hee can be used n the pocess plannng of bong opeatons wth nseted bong heads so that the suface fnsh and dmensonal qualt of the holes ae mantaned b avodng ecessve foced vbatons

29 Howeve, the ente poposed models have been appled onl to the lmted aeas of the machnng pocesses and have not et consdeed the vefcaton of the geneated faces. Tang and Sasahaa 7, 8a and Tang et al. 8b have poposed an nvestgaton of themal behavo and machnng eo esultng fom the cuttng foces and themal epanson on clnde lne dung ts bong pocess. The eseach was conducted on the effect of cuttng condtons on tempeatue se of clnde lne dung clnde-bong pocess. The nfluence of the cuttng condtons fo eample: cuttng speed, feed ate, depth of cut, cuttng flud on the cuttng foces and tempeatue dstbuton n a clnde dung machnng was nvestgated, and the heat patton flowng to the wokpece unde vaous cuttng condtons especall, unde hgh-speed cuttng, wth a mamum cuttng speed up to 9 m/mn was then detemned. thee-dmensonal FEM analss model was developed to smulate the tempeatue dstbuton n the clnde lne and themal epanson of the clnde lne dung machnng. Then, the sutable cuttng condtons n clnde bong wee confmed b FEM analss. Howeve, the ente poposed model dd not deal wth how the ndvdual models ae ntegated to estmate the fnal geometes of the machned pats b consdeng the nseted tools n accodance wth the ntenatonal tool geomet standads. Kamakc et al. have poposed a unfed cuttng foce model fo tunng, bong, dllng and mllng opeatons wth the nseted tools. The nseted tool tps and the oentatons to the efeence tool coodnates ae mathematcall epesented b Intenatonal Standadaton Oganaton ISO tool defnton standads. The fcton foces actng on the ake faces ae tansfomed nto efeence tool coodnates usng the geneal tansfomaton mat. The mateal and nset geomet-dependent fcton and nomal foces ae tansfomed nto a common efeence fame followed b the opeaton specfc machne coodnates. It s shown that one unfed model s capable of pedctng foces fo multple metal cuttng opeatons. The genealed modelng of metal cuttng opeatons allows the smulaton of pat machnng wth multple opeatons and vaous tools. The model wll be etended to develop unfed chatte stablt laws fo multple opeatons. Howeve, the poposed model dd not deal wth how the ndvdual models ae ntegated to estmate the fnal geometes of the boed faces, the geometc devatons and the suface oughness n the vtual machnng pocesses. lthough etensve eseach has been conducted to develop seveal models n vtual machnng, focusng on development of models fo bong pocesses, Howeve, the vtual machnng of pats b consdeng the phscs of the bong pocesses ncludng knematc moton devatons of machne tools as elatve moton between the tool and wokpece, whch ae deepl nfluenced b the geometc devatons of the poducts, has not et been clafed. Theefoe, t s now equed to claf the elatonshps between the knematc moton devatons of the machne tools and the geometc devatons of models of the bong pocesses. In the pesent eseach, the vtual machnng n bong pocesses s poposed to smulate model of the machne tools and the machnng pocesses n ode to estmate and to vef the geometc devatons of the boed faces - 6 -

30 on CNC machnng centes. The poposed hee epesents the bong pocesses based on both the shape geneaton motons b consdeng the machne tool coodnate sstems accodng to ISO 3- latest ssues and the cuttng tool geometes n accodance wth the ntenatonal tool geomet standads... Tunng pocess modelng Consdeable wok has been epoted on vtual machnng modelng of tunng pocesses. The motvaton fo most of ths eseach has been mpoved smlat wth the bong pocesses n numecal analss and paamete pedcton such as cuttng foces estmaton, machnng eo, feed, tempeatue etc. Hong and Ehmann 995 have poposed a method fo geneatng engneeed sufaces b the suface-shapng sstem. The method defned a genealed analtcal model and pocedue fo the smulaton of the suface geneaton pocess. The basc dea of the suface geneaton pocess s ntoduced fst. Then, the cuttng tool geomet s defned. Geneal concepts of cuttng tool geomet ae appled to the majot of metal emoval based suface geneatng pocesses. Specfcall, the majo cuttng edge egon s defned b a suface-suface ntesecton algothm and the cuttng angles ae obtaned along the majo cuttng edges. Theeafte, b mpovng the estng method fo modelng machne tool knematcs, emboded n the model of the "fomshapng sstem" poposed b Reshetov and Potman 988. The pape also pesented an applcaton of the method of the suface-shapng sstem of n tunng pocesses. Howeve, the pape does not dscuss how the ndvdual models ae combned to obtan the fnal geomet of the tuned faces ncludng nseted tool tps, and the oentatons to the efeence tool coodnates ae mathematcall epesented b ISO tool defnton standads. In late eseach of the vtual machnng n tunng pocesses, seveal eseaches have poposed the smulaton of cuttng foce models. Rao and Shn 999 have poposed dnamc cuttng foce pocesses fo the thee-dmensonal o oblque tunng opeaton chatte pedcton n tunng. The dnamc foce model was mplemented on a compute to geneate tme-savng chatte pedctons. Wang has poposed a development n pedctng the chp flow decton and cuttng foce models fo tunng opeatons. The model s pesented whch pedcts the chp flow decton n tunng opeatons wth nose adus tools unde oblque cuttng condtons. The model pesented onl the tool cuttng edge geomet and the cuttng condtons feed and depth of cut. The pape also compaed the esults of epements whch have vefed the chp flow model and shown that the model s pedctons ae n good ageement wth the epemental esults. Budak and Olu 7 have poposed an analtcal model fo the pedcton of the stablt lmt n tunng and bong opeatons. The model povdes a multdectonal appoach to the dnamc sstem b solvng the stablt lmt n a mat fom. In addton the tue geomet of pocesses,.e. the mpotant cuttng angles and the nset node adus, ae ncluded n the model. Kamakc et al. have poposed a unfed cuttng foce - 7 -

31 models fo tunng, bong, dllng and mllng opeatons wth the nseted tools. The nseted tool tps and the oentatons elatve to the efeence tool coodnates ae mathematcall epesented b ISO tool defnton standads. The model can be appled to the cuttng foces pedcton n tunng pocesses whch ae smla to bong pocesses. Howeve, the ente poposed model of the vtual machnng n tunng pocesses focuses on cuttng foces, and dd not deal wth how the ndvdual models ae ntegated to estmate the fnal geometes of the tuned faces, the geometc devatons and the suface oughness n the vtual machnng pocesses. lthough etensve eseach has been conducted to develop seveal models n vtual machnng, focusng on development of models fo tunng pocesses, Howeve, the vtual machnng of pats b consdeng the phscs of the tunng pocesses ncludng knematc moton devatons of machne tools as elatve moton between the tool and wokpece, whch ae deepl nfluenced b the geometc devatons of the poducts, has not et been clafed. Yao et al. 6 have poposed a modelng of vtual wokpece wth machnng eos epesentaton n tunng. B analng and modelng the fomng pocess of wokpece and the eo souces contbutng to machnng pecson of wokpece n tunng opeaton, the cutte tajecto and atttude epesentaton CT_Rep s pesented to chaactee the geometc eos of machned wokpece n vtual machnng. Then a suface topogaph smulaton model s establshed to smulate the suface fnsh pofle geneated afte a tunng opeaton. Zhu et al. 7 have poposed eseach on vtual NC technque n tunng and mllng pocess. The geomet smulaton and phscs smulaton ae ealed b vtual NC technque n tunng and mllng pocess. The eseach demonstates that the smulatons ae handled to complete the vtual machnng of the poduct b checkng machnng ablt, atonalt of desgn, pedcton manufactue ccle, and pomptl modfng desgn. nand 8 has poposed a statc eo modelng n tunng opeaton and ts effect on fom eos n hs Maste s thess. Ths eseach eamnes the effect of such eos on pat geomet poduced b a tunng opeaton. The statc eos consdeed n ths eseach ae the machne bed eos usuall efeed to as geometc eos. These eos ae pesent n the machne n the cold stat condton and ae nduced ove a peod of tme due to gadual weang and msalgnment. Ths eseach also ncludes modelng the spndle eo as a sgnfcant souce of pat suface devaton fom deal geomet. Ramaswam has poposed an ntegated famewok fo vtual machnng and nspecton of tuned pats n hs Ph.D Thess. The eseach pesented n hs dssetaton focuses on a two-stage methodolog of vtual machnng of pats poduced on a thee-as tunng cente and vtual nspecton of the poduced pats usng a bdge-tpe coodnate measung machne CMM. The vtual machnng sstem focuses on a po pedctng the suface pofle of the - 8 -

32 tuned pat. The suface pofle s geneated b modelng the effects of the statc eos nheent n the tunng cente, the eo n the spndle moton, machne vbatons, tool geomet, pocess paametes, and tool wea. Howeve, the ente poposed model of the vtual machnng n tunng pocesses focuses on machnng eos and do not deal wth how the ndvdual models ae ntegated to estmate the fnal geometes of the tuned faces whch consde both the shape geneaton motons b consdeng the machne tool coodnate sstems accodng to ISO 3- latest ssues, and the cuttng tool geometes n accodance wth ntenatonal tool geomet standads. In ths eseach, the vtual machnng n tunng pocesses have been used to smulaton model of the machne tools and the machnng pocesses, n ode to estmate and to vef the geometc devatons of the tuned faces n the machnng pocesses of CNC tunng centes and sngle pont tools. The model poposed hee epesents the tunng pocesses based on both the shape geneaton motons b consdeng the machne tool coodnate sstems accodng to ISO 3- latest ssues, and the cuttng tool geometes n accodance wth ntenatonal tool geomet standads..3 Thee-Dmensonal Suface Roughness In the pesent global the compettons, manufactung pocesses n ndust ae developng contnuous to ncease the qualt and the elablt of the poducts and to decease the cost of manufactung pocess opeatons. In geneal t s poblematc to detemne the values of the pocess paametes n pactce and mame the manufactung sstem pefomance usng the avalable esouces. Benados and Vosnako 3 have evewed and descbed two man pactcal poblems that engnees face n a manufactung pocess. The fst s to detemne the values of the pocess paametes that wll eld the desed poduct qualt meet techncal specfcatons and the second s to mame manufactung sstem pefomance usng the avalable esouces. To ovecome these poblems, the eseaches popose models that t to smulate the condtons dung machnng and establsh cause-effect elatonshps between vaous factos and desed poduct chaactestcs. Futhemoe, the technologcal advances n the feld, fo nstance the eve-gowng use of compute contolled machne tools, have bought up new ssues to deal wth, whch futhe emphase the need fo moe pecse pedctve models. Suface oughness s a wdel used nde of poduct qualt and n most cases a techncal equement fo mechancal poducts Benados and Vosnako, 3. The suface fnsh of a machned pat s one of the most mpotant poduct qualt chaactestcs. Suface oughness geatl nfluences the mechancal and phscal popetes of contactng pats. The undestandng of ths behavou s mpotant n man applcatons such as wea, fcton, lubcaton, sealng tghtness of jont, contact gdt, contact stess, loaded aea - 9 -

33 and themal conductvt. Theefoe, engnees ae ve concened about the suface oughness of the poducts Dong, et al., 99. The development of new ndustes has led to a equement fo supe-smooth sufaces and fo the ablt to measue sufaces of ndustal pats accuatel and to pedct sufaces of pats accuatel befoe eal machnng pocesses. Thee ae man eseaches wokng n the aea of pedctng suface oughness n machnng. Benados and Vosnako 3 have evewed and defned fou majo categoes/appoaches. These ae: ppoaches that ae based on machnng theo to develop analtcal models and/o compute algothms to epesent the machned suface Ref. Gesk, 996; Ln and Chang, 998; Baek, et al., ; ppoaches that eamne the effects of vaous factos though the eecuton of epements and the analss of the esults Ref. bouelatta and Madl, ; Ghan and Choudhu, ; Shou and Chuang, ; 3 ppoaches that use desgned epements Ref. Davm, ; Kopac, et al., ; Dabnun, et al., 5; Davdsona, et al., 8; Shahom, et al., 3; 4 tfcal ntellgence I appoaches Ref. Rsbood, et al., 3; Jao, et al., 4; Oktem, et al., 6; Davm, et al., 8; sltuk and Cunkas, ; Bhaath Raja and Baska,. Keepng n lne wth objectves of the pesent eseach, the lteatue evew wll focus on aspects of the appoaches that ae based on machnng theo to develop analtcal models and/o compute algothms to epesent the machned suface. The models to estmate the suface oughness has placed emphass on cetan aspects such as pocess knematcs, cuttng tool popetes, chp fomaton mechansm etc. Vtual machnng s utled so as to acheve the goal of buldng a model that wll be able to smulate the ceaton of the machned suface pofle, thus vsualng suface topogaph and assessng suface oughness. Theefoe, seveal eseaches have focused on development of models fo machnng theo to develop analtcal models and/o compute algothms n ode to estmate the suface oughness as dscussed below. Ehmann and Hong 994, 995 have poposed a new method to epesent the suface geneaton pocess, whch the called "suface-shapng sstem" b mpovng and etendng the estng method fo modelng machne tool knematcs emboded n the model of the "fomshapng sstem FSS" b Reshetov and Potman 988. The poposed suface-shapng sstem model facltates the evaluaton and smulaton of the suface tetue of machned components b accountng fo ealstc tool geomet and machne knematcs condtons. Lee et al. have focused on pedcton of suface oughness and pofle n hgh-speed end mllng. method fo smulatng the machned suface was pesented usng the acceleaton sgnal nstead of the cuttng foces. The agument povded was that the vbaton, whch s caused b the hgh speed of the spndle, deteoates the geometc accuac of the machned suface. geometc end mllng model was used fo modelng the end mll offset and tlt angle. - -

34 The compute algothm was developed n tems of cuttng condtons, cutte and wokpece geomet, and unout paametes to detemne the angula poston of the end mll. Howeve, the ente eseach as epoted dd not nclude smulaton of the 3-dmentonal geomet of boed and tuned faces n ode to estmate 3-dmensonal suface oughness ncludng knematc moton devatons. The cuttng tool geometes ae mathematcall epesented b ISO tool defnton standads and ae mpotant value paametes fo estmaton of suface oughness. It s ecogned that poflng technques have been wdel used n ndust and academc eseach fo manufactung contol and functonal contol of suface oughness. In some cases, howeve, the poflng technques and two-dmensonal D paametes defned n standads ae nadequate and/o unsutable fo chaacteng sufaces. In ecent eas, thee has been an nceasng need fo the chaacteaton of suface topogaph n thee dmensons 3D. Theefoe a cleal defned, effectve and wdel accepted 3D paamete set s ugentl equed Dong, et al., 994. The estmaton of 3D suface oughness of machned pats befoe eal machnng pocess s mpotant fo the desgn and the manufactung pocess of poducts. Dong et al. 99, 994 have poposed a compehensve stud of paametes fo chaacteng thee-dmensonal suface topogaph. The stud has dscussed the poblem of D paamete vaaton though the analss of 3D suface topogaph and dscussed paametes whch ae suggested to fom the bass of a pma paamete set fo chaacteng ampltude and some functonal popetes. In late ea, Dong et al. 995 have dscussed efeence planes fo suface oughness assessment n 3D. Fom a standadaton pont of vew, efeence planes fo assessng nomnall flat and cuved sufaces ae ecommended though theoetcal analss of algothms and vefcaton of epemental esults. Bakolas 3 has poposed a pocedue fo numecal geneaton of ough sufaces wth pescbed statstcal and spectal popetes. The pocedue etends the method of the lnea tansfomaton of mat, fst poposed b emplong the non-lnea Conjugate Gadent Method CGM and Fast Foue Tansfoms FFT n ode to be n poston to take nto consdeaton sgnfcantl lage potons of the autocoelaton functon CF, thus mpovng the ageement between the spectal chaactestcs of the geneated sufaces and the pescbed values. The method s capable of poducng abta oented sufaces b usng an CF that s otated aound ts ogn. The esults show that the method can adequatel poduce ough sufaces whose statstcal and spectal chaactestcs match the pescbed values Qunsat et al. 8 have poposed a 3D suface oughness paamete that fomales the elatve nfluence of both machnng paametes and suface equements. The poposed has focused on fee-fom suface machnng whch bult b consdeng that dung the mllng opeaton, the cuttng edges undego a combned moton of tanslaton and otaton. Smulatons seve to defne a suface oughness paamete coelated wth the machnng stateg. Valdatons - -

35 ae caed out subsequent to the thee-as mllng usng a ball end cutte tool of plane sufaces unde vaous cuttng condtons va the epemental measuements of suface oughness. Recentl, Buj-Coal et al. have poposed a suface topogaph n ball-end mllng pocesses as a functon of feed pe tooth and adal depth of cut. The numecal model was developed to pedct topogaph and 3D suface oughness based on geometc tool-wokpece ntesecton. It allows detemnng suface topogaph as a functon of feed pe tooth and evoluton, adal depth of cut, aal depth of cut, numbe of teeth, tool teeth ad, hel angle, eccentct and phase angle between teeth. Howeve, the ente poposed model of the estmaton of 3D suface oughness dd not consde the knematc moton devatons ae ntegated to estmate the fnal geometes of the boed and tuned faces. Theefoe, the vtual machnng of bong and tunng pocesses ncludng knematc moton devatons has been used to develop smulaton model n ode to estmate and to vef the 3D suface oughness of the boed and tuned faces..4 Thee-Dmensonal Toleances Manufactung toleances ae ntended to detemne the ntemedate geometcal and dmensonal states of a manufactued pat dung ts manufactung pocess. Manufactung toleances seve to satsf not onl the functonal equements gven n the poduct defnton model, but also the manufactung constants, such as machne accuac and mnmum eta machnng thckness Zhang and Qao, 3. Theefoe, manufactung toleances have to detemne the toleance analss n ode to estmate the accumulaton of the desgn toleances on component dmensons and featues to ensue that pats wll assemble dung poducton. Toleance analss s an essental pat fo mechancal desgn and manufactung because t affects not onl the pefomance of poducts but also the cost. Ove the last tht eas, a lage amount of fundamental eseach effots has been gven to eploe the mathematcal bass fo toleance analss. compehensve evew of dmensonng, toleancng, and analss pocesses ma be found n Ro et al. 99 and Ngam and Tune 995. Ths wok wll povde an ovevew of po eseach. Fo toleance epesentaton, the models o concepts such as: the wost case toleance analss Dantan and Quesh, 9; Mansu, et al.,, 3, statstcal appoaches to toleance analss Sugmua and Nakamoto, 3; Rout and Mttal, 6; Gonale and Sanche, 9; Beaucae, et al., 3, Monte Calo smulatons Buee, et al., 7; Wu, et al., 9; Wu, et al., and compute aded toleance analss tool s pesented that asssts the desgne n evaluatng wost case qualt of assembl afte toleances have been specfed Salomons, et al., 996a, 996b; Tessande, et al., 999; Chabet and Olando, 4; nselmett, et al.,. Howeve, as new geneatons of toleancng standads,.e., SME Y4.5-9 and ISO : wee eleased and populaed, geometc toleances ae geneall accepted as - -

36 ndust pactces. The tadtonal one dmensonal D o two dmensonal D toleance analss models ae nsuffcent to meet the eve-tghtenng and nceasngl comple equements of toleance analss n vaous felds. Moe specfcall, vaatons of a featue caused b geometc toleances ae thee dmensonal, whch cannot be consdeed b /D methods. Theefoe, eseaches and engnees need a new method that can anale how those geometc toleances ae epesented and popagated n thee dmensonal space ugentl Chen, et al., 4. Recentl, Chen et al. 4 have poposed a compehensve evew stud of 3D toleance analss methods, whch evews fou majo methods of 3D toleance analss and compaes them based on the lteatues publshed ove the last thee decades. The methods studed ae Toleance-Map T-Map, mat model, unfed Jacoban-Toso model and dect lneaaton method DLM, all of whch ae eseach hotspots ecentl. Keepng n lne wth objectves of the pesent eseach, the lteatue evew wll focus on aspects of the mat model whch uses a dsplacement mat to descbe the small dsplacements of a featue wthn the toleance one and the cleaance between two featues. Ths model, completed b a set of nequaltes defnng the bounds of the toleance ones, epoduces the measuable o non-nvaant dsplacements assocated wth vaous tpes of toleance. It s ve effcent fo computaton and can easl be ntegated nto CD sstems. Some of the ke papes n the aea of 3D toleance analss n mat models ae dscussed below. The mat model ntoduced b Clement et al. 99, 993 and 994, Desoches and Rvbet 997. Clement et al. 99, 993 and 994 have poposed a theo and pactce of 3D toleancng fo assembl n CD/CM sstems whch s called Technologcall and Topologcall Related Sufaces TTRS appoach. In ths appoach, toleances ae teated as small dsplacements. Desoches and Rvbet 997 have poposed a mat appoach to the epesentaton of toleance ones and cleaances. The model uses a dsplacement mat to descbe small dsplacements of a featue wthn the toleance one and the cleaance between two featues. The mat s done usng the homogeneous tansfoms commonl assocated wth obotc modellng. Ths mat epesentaton s completed b a set of nequaltes defnng the bounds of the toleance ones. It s woth mentonng that some compute aded toleancng softwae CTs based on the mat model have been developed and appled successfull, such as CTI.3D FDT Psco and Goleo,, FROOM Salomons, et al., 996a, 996b and the Quck GPS Geometcal Poduct Specfcaton sstem has been developed n a CTI V5 nselmett, et al.,. The statstcal method of the mat model fo toleance analss can be found n Whtne et al Sugmua et al. 3 and Satonaka et al. 5a, 5b, 7a have poposed a stud of statstcal analss of 3D geometc toleances of poducts. The objectve of the pesent eseach s to develop a sstematc method fo plannng and analng geometc toleances of - 3 -

37 thee-dmensonal mechancal poducts. The analses of the geometc devatons of the taget featues aganst the oot datum featues ae caed usng the Monte-Calo smulaton method. The 3D geometc toleances ae estmated usng the statstcal devatons of the postons and the oentatons of the geometc featues, based on the devaton paametes and the elatonshps between the datum featues and the taget featues. In patcula, emphass s gven to the analss of the statstcal devatons of the geometc featues unde the MMC Mamum Mateal Condtons, whch specfes the nteacton between the dmensonal toleances and the geometc toleances. s egads the dmensonal toleances and the geometc toleances, amed at ealng sstematc analss and desgn methodologes fo the thee dmensonal poducts as mentoned above. The analses of knematc moton devatons of machnng centes based on geometc toleances have not et been dscussed. Satonaka et al. 7b, 8 have appled and developed the mathematcal analss of 3D geometc toleance fom Sugmua et al. 3 to the analss of knematc moton devatons of 3-as machnng centes based on geometc toleances. The geometc devatons of the gudewas wee dscussed, and a method was poposed to estmate the standad devatons of the geometc devatons of the gude-was. The geometc devatons of the lnea tables wee fomulated, based on the potes among the gude-was of the lnea tables. Howeve, the latest eseach wok has not et dscussed the knematc moton devatons based on geometc toleance of the ota tables whch ae not lnea aganst the otatonal angles of the tables. In ths eseach, mathematcal models epesentng the knematc moton devatons of the ota tables and the 5-as machnng centes ae establshed. The models ae based on the 3D geometc toleances of the components, and estmaton of 3D toleances fom the vtual machnng of the CNC machnng centes n bong pocesses and the CNC tunng centes n tunng pocesses ncludng knematc moton devatons

38 Chapte 3 Smulaton of Vtual Machnng Sstems n Bong and Tunng Pocesses - 5 -

39 3. Smulaton of Vtual Machnng Sstems n Bong and Tunng Pocesses 3. Intoducton s dscussed n Secton.3, ths chapte focuses on the pat manufactung pocesses n a vtual manne b ncopoatng the effects of vaous factos of machnng pocesses. vtual machnng sstem descbed below epesents vtual machnng pocesses of the bong pocess on CNC machnng centes and tunng pocess on CNC tunng centes, and smulated pats ae geneated takng nto consdeaton of knematc moton devatons due to spndle moton eos and geometc eos of nseted cuttng tools. The pats thus geneated can be vewed as a epesentatve of an actual pat machned on that machne and can be used to evaluate the 3D suface oughness and toleance on the geomet of the pat. Fgue 3- llustates the mpotant components of the vtual machnng sstem n the contet of the oveall sstem. Fg. 3- Ke components of the vtual machnng sstem The ke components of the vtual machnng sstem n ths chapte ae: Modelng of shape geneaton motons Machne tool coodnate sstems, poston and oentaton eos n accodance wth ISO 3-: - 6 -

40 Knematc moton devatons n bong pocesses Knematc moton devatons n tunng pocesses Geneaton of smulated pats Detals of these models ae povded below: 3. Modelng of Shape Geneaton Motons Fgue 3- summaes the factos whch affect the machnng eos of the poduct sufaces and the elatonshps fom the vewpont of the shape geneaton pocesses of the machne tools. The geometc eos of the poduct sufaces ae detemned manl fom the elatve moton eos between the tools and the wokpeces, the geometc eos of the tools, and the eos n the mateal emoval pocesses. The equements of the geometc accuac of the poduct sufaces ma not be satsfed due to the factos ognated fom the stuctual desgn and the manufactung pocesses of all the components of the machne tools. The elatons among the factos shown n Fg. 3- ae ve complcated, and ae not et clea Sugmua and Muabe, 997. Theefoe, ths secton deals manl wth the knematc moton eos n elatve motons between the tools and wokpeces. Fg. 3- Factos affectng machnng eos Sugmua and Muabe, 997 The shape geneaton pocesses of the machne tools ae geneall epesented b the shape geneaton motons, and also the tool geometes Reshetov and Potman, 988; Sugmua, et al., 98. The shape geneaton motons, whch ae the elatve motons of the tools aganst the wokpeces, ae eecuted b a set of gd component of the machne tools. Fgue 3-3 shows a schematc llustaton descbng the gd components called unts element and the shape geneaton motons among them. Fgue 3-4 shows chan-lnk dagam epesentng the shape geneaton motons; S, S,, S l epesent the lnks, S s the pat to be machned, S l s the cuttng tool, and S,, S l- ae the ntemedate lnks; q, q,, q l ae moton paametes of the unts; k, k,, k l ae the elatve moton of the unts

41 S S S k k j j Sl S l k l jl Fg. 3-3 Mathematcal model of machne tool Mowak, 8 k k k 3 k l q q q 3 q l Fg. 3-4 Chan-lnk dagam epesentng the shape geneaton motons Potman and Inasak, Homogeneous pont of coodnates Vectos of fouth ode of ponts n a thee-dmensonal space ae dvded nto two classes dependng upon the geometcal phscal natues: egenvectos and non-egenvectos. Pont adus vectos belong to the fst catego, and vectos obtanable b dffeentaton o nfntel small tansfomaton of adus vectos belong to the second catego. The coodnates of the vectos of the fouth ode ae called homogeneous coodnates. Egenvectos have a fouth homogeneous coodnate equal to unt, and non-egenvectos have a fouth homogeneous coodnate equal to eo. The adus vectos of the ponts wth Catesan coodnates,, ae wtten n the fom of a column vecto of the fouth ode - 8 -

42 3- Futhemoe, n ode to save space, we shall wdel use the epesentaton of the column n tansposton fom,.e., n a fom of a ow vecto,,, T, whee T s the sgn of tansposton. Vecto can be epesented as 3 e e e e 4, whee e, e, e 3 ae unt vectos of the aes of the coodnates; e, e, e 3, e 4 s the adus vecto of the ogn of the coodnates; e 4,,, T. 3- The onl opeaton that tansfoms the adus vecto nto anothe adus vecto s multplcaton of the adus vecto b the mat of tansfomaton of the coodnates. B defnton of the adus vecto, ts ogn alwas concdes wth the ogn of the coodnates Reshetov and Potman, Tansfomaton of coodnates Tansfomaton of coodnates, consde two sstems of coodnates S - and S. The same pont n space has dffeent coodnates n these sstems wth the ecepton of the tval case when S - and S completel concde. Denote b and l the adus vectos of the tpe Eq. 3- of a pont n the two-coodnate sstems, the ae lnked b the mat elaton j q,q,..., ql l 3-3 whee, - 9 -

43 l j : Poston vecto of a pont on the tool gven n the tool coodnate sstem, : Poston vecto of the pont gven n the wokpece coodnate sstem, and : The coodnate tansfomaton mat of ode 4 4 havng the followng stuctue: a a a 3 a a a 3 a a a a4 a 4, a n whch the uppe left 3 3 block descbes the otaton of sstem S elatve to ts ogn of coodnates O to such a poston that the aes of sstems S - and S become paallel and smlal dected. Hence, t follows that ths block epesents an othogonal mat,.e., fo all, k,, 3, 3 a a 3 a a, f k,, f k j kj j jk j j, and, futhemoe, the detemnant of ths mat s a a a 3 a a a 3 a a a The fst thee coodnates a 4, a 4 and a 34 of the fouth column of mat ae Catesan coodnates of the ogn O of sstem S n sstem S -. Let sstems S - and S be ted wth two consecutve shape geneaton lnks that the elatve motons of the lnks ae lmted to s of the smplest motons, fomula Eq. 3-3 can be epesented as: l α j q,q,..., ql β γ 3-5 whee, α γβ : 44 tansfomaton matces epesentng knematc motons and postons α,..6 : Indces epesentng the dectons of knematc moton and postons., and 3 means lnea motons and postons of, and dectons, espectvel. 4, 5 and 6 means ota motons and postons aound, and dectons, espectvel. β : Values of knematc motons and postons γ : Indces epesentng coodnate sstems - 3 -

44 - 3 - The ndvdual elatve motons gven b α ae geneall ethe the tanslaton motons along the, Y and Z-as o the ota motons aound the, Y and Z-as. The tansfomaton matces ae descbed b the matces shown n Table 3-. Table 3- Tansfomaton matces descbng tanslaton motons and ota moton Sugmua and Muabe, 997 Moton Tpe s Relatve Moton Tansfomaton Mat Tanslaton Moton Y Z 3 3 Rota Moton B C cos sn sn cos 4 ϕ ϕ ϕ ϕ cos sn sn cos 5 ψ ψ ψ ψ cos sn sn cos 6

45 3..3 Homogeneous tansfomaton mat HTM of otatonal and tanslatonal eos To stud the eo behavou of a machne movement, the knematc model of the machne s developed n the fom of a sees of HTM. In ths model, each tpe of eos s defned and analsed b usng the HTM model to detemne the effect of the eos on the cuttng-pont postonal accuac wth espect to the wokpece. Consde the smple case of a lnea as moton, the caage moves along the Y-as to a pont, b,, as shown n Fg Fg. 3-5 Lnea moton caage n Y-as Nedno, 999 The N'-fame s defned as pue tanslaton movement and the ogn pont of N'-fame s defned as pont O N' whch s offset, b, fom the ogn pont of R-fame. The HTM of the N'-fame wth espect to the R-fame s the HTM of n Table 3-, the esult s: b R N 3-6 Fo an lnea moton, a gd bod wll alwas have 6 eo components whch consst of thee otatons,, and thee tanslatons,,, see Fg To undestand these eos, the N"-fame and the N-fame ae defned whee the N"-fame s pue tanslaton espect to the N'-fame and has an offset of,, fom the ogn of the N'-fame. The N-fame s pue otaton wth espect to the N"-fame and ts ogn pont s on the ogn pont of the N"- fame. The HTM of pue tanslaton can be found b multplng equatons n Table 3- n tansfomaton mat of, and 3 as show the Eq The HTM of thee otatons can be - 3 -

46 found b multplng equatons n Table 3- n tansfomaton mat of 4, 5 and 6, as show n the Eq. 3-8, and E j s the nfntesmal mat of the poston eos of the th lnk.,, Fg. 3-6 S eos of sngle as lnea moton Nedno, 999 E N N 3-7 E N N c c s c s s c c s s c c s s s c s s s c s c c s s s c c c 3-8 whee: c cos ; s sn ; c cos ; s sn ; c cos ; s sn

47 Because the angles of these otatng eos ae ve small, most ae n mnutes of ac, these appomate values can be adopted: c c c c c c ; s c s c ; c s c s ; c s c s ; c s s s s s s s s s c ; So, the HTM fo those s eo paametes n Eq. 3-8 s: E N N 3-9 These 6 eo paametes of the lnea movement that s shown n Eq. 3-9 ae known as: : Poston eo, wth deflecton n the decton of feed : Staghtness eo n -as decton : Staghtness eo n Z-as decton : ngula eo about the Y-as Roll movement; otaton about the feed as : ngula eo about the -as Ptch o Tp movement; otaton about one as n the plane of the table pependcula to the feed as : ngula eo about the Z-as Yaw o Rota movement; otaton nomal to the plane of the table. The HTM of the N-fame espect to the R-fame fo the lnea movement n the Y-as to pont, b, whch nclude all eos s: R RN b E N N N RN _ actual b 3- These paametes ae functons of the postons of the caage n the efeence fame. B measung these paametes along the movng as, the actual poston of an pont on the caage fame N-fame can be tansfomed nto the efeence fame R-fame Nedno,

48 S of these paametes whch can be used the knematc moton devaton fo smulaton n the vtual machnng s gven andoml, nomal dstbuton. 3.3 Machne Tool Coodnate Sstem, Poston and Oentaton Eos lthough the nomenclatue fo the machne aes of moton s defned ISO 84, mee labellng of the aes s not adequate fo the puposes of the chaacteaton of machne geometc eos and the compensaton fo the effects usng machne tool contolles. Ths secton topc povdes a sstematc wa to defne a machne tool coodnate sstem n accodance wth ISO 3-: n ode to geneate the vtual machnng, n whch the geometc elatonshps ae among the aes of moton and assocated eos. B descbng the postons and oentatons of the aes of moton n a coodnate sstem, the algnment eos among these aes, necessa fo geometc accuac evaluaton and/o softwaebased eo compensaton, can be dentfed fo an machne stuctual confguaton. To elmnate edundant algnment eo measuements among the aes of moton, the ogn and oentaton of the machne tool coodnate sstem s chosen to oentate wth the pma as of moton defnng two oentatons and the seconda as of moton defnng the thd oentaton ISO 3-:. In ths eseach, the poposed machne tool coodnate sstem s the coodnate sstems on 3- as machnng centes of bong pocesses and CNC tunng centes of tunng pocesses 3.3. Machne tool coodnate sstem of bong pocesses The bong pocesses on 3-as machnng centes ae caed out b both the spndle otatons and the lnea feed moton along Z-as, theefoe, the moton devatons of the spndle otaton s an mpotant ssue fo evaluatng the geometc devatons of boed holes. The coodnate sstems fo the bong pocesses ae set accodng to ISO 3-: b consdeng n the efeence staght lne of the lnea as of moton and as the otaton. s pescbed b ISO 84, the machne coodnate sstem s a ght-hand ectangula sstem. The poston and oentaton of the machne tool coodnate sstem s tpcall defned b the aes of moton of ts movng components. The coodnate sstems fo the bong pocesses ae shown n Fg The efeence coodnate sstem O R s set accodng to ISO 3-:, and the othe coodnate sstems ae as follows. The coodnate sstem O S of the spndle s fed on the spndle and has fou devaton paametes epesentng the poston and oentaton devatons of the aveage otatonal as

49 of the spndle. The ae C, C, and whch epesent the postonng devatons n - and Y-as and the otatonal devatons aound - and Y-as. The coodnate sstem O B of the bong ba s fed on the bong ba and the paamete B gves the dstance between O s and O B epesentng the length of the bong ba. 3 The coodnate sstem O T of the tool tp s fed on the tool tp and the paamete R T gves the dstance between O B and O T epesentng the adal poston of the tool tp aganst the bong ba as. 4 The coodnate sstem O E of the cuttng edge s fed on the cuttng edge and the paametes R E and E gves the dstance between O T and O E epesentng the shapes and the dmensons of the tool tp. R s O s Y s O R R s Y R C B Z B O B B Y B T T O T R T Y T Fg. 3-7 Coodnate sstems fo bong pocesses

50 3.3. Machne tool coodnate sstem of tunng pocesses The tunng pocesses on CNC tunng centes ae caed out b the spndle otatons, the lnea feed moton along the Z-as and the depth of cut along the -as, theefoe, the moton devatons of the spndle otaton, feed moton and depth of cut ae mpotant ssues fo evaluatng the geometc devatons of tuned pats. The coodnate sstems fo the tunng pocesses ae set accodng to ISO 3-: b consdeatons descbed fo the efeence staght lne of the lnea as of moton and as of the otaton. The coodnate sstems fo the tunng pocesses on CNC tunng centes ae shown n Fg The coodnate sstems O S, O R, O CR, O CS, O T and O E ae set accodng to ISO 3-:. The tunng pocesses ae caed out b the spndle otatons, the lnea feed moton along Z-as and the depth of cut along -as, and the othe coodnate sstems ae as follows. The coodnate sstem O S of the spndle s fed on the spndle and has two devaton paametes epesentng the oentaton devatons of the aveage otatonal as of the spndle. The ae and whch epesent the otatonal devatons aound - and Y-as. The coodnate sstem O CR of the caage s fed on the mddle and below the caage and the paamete gves the dstance between O s and O CR epesentng the length of the movng caage along Z-as. 3 The coodnate sstem O CS of the coss slde s fed on cente of the coss slde, the paamete gves the dstance between O CR and O CS epesentng the length of the movng coss slde along -as, the paamete L and L epesentng the length of the coss slde as aganst the tool tp. 4 The coodnate sstem O E of the cuttng edge s fed on the cuttng edge and the paametes E and E gves the dstance between O T and O E epesentng the shapes and the dmensons of the tool tp. a Stuctues of CNC tunng centes

51 L CS Z CS O CS L CR T S R O S Z S O Z R R O T Z T O CR Z CR T E e O T Z T E O E Z E E Detal b Coodnate sstems of tunng pocesses Fg. 3-8 Stuctues and coodnate sstems fo tunng pocesses 3.4 Knematc Moton Devatons n Bong Pocesses 3.4. Shape geneaton motons n bong pocesses The bong pocesses on CNC machnng centes ae caed out b both the spndle otatons and the lnea feed moton along Z-as, theefoe, the moton devatons of the spndle otaton s an mpotant ssue fo evaluatng the geometc devatons of boed holes. RS SB BT TE Fg. 3-9 Coodnate sstems and the devatons of bong pocesses Fve catesan coodnate sstems shown n Fg. 3-9 ae set to epesent the knematc moton devatons whch ae n accodance wth Fg The ae, O R, O S, O B, O T and O E whch epesent the coodnate sstems of the efeence, spndles, bong bas, tool tps and cuttng edges, espectvel

52 The shape geneaton pocesses of the machne tools ae geneall epesented b the shape geneaton motons, and also the tool geometes. The shape geneaton motons, whch ae the elatve motons of the tools aganst the wokpeces, ae eecuted b a set of gd component of the machne tools Sugmua and Muabe, 997. The shape geneaton motons of the cuttng edge aganst the efeence ae descbed b Eq. 3-. R RS SB BT TE E 3- whee, j : 4 b 4 homogeneous tansfomaton matces epesentng the elatve postons and the knematc motons between pas of gd bodes and j E : Poston vecto of a pont on the cuttng edge n the cuttng edge coodnate sstem. R : Poston vecto of the pont on the cuttng edge n the efeence coodnate sstem. The ndvdual matces nclude some knematc and poston devatons due to both the moton eos and the set-up eos, theefoe, the knematc moton devatons n the bong pocesses dscussed n the followng equaton s obtaned fom Eq. 3- b applng the paametes mentoned above R E ERSRS E SB B BT RT TE E TE E 3- whee, E : Postonng devatons and staghtness devatons n Z-as E RS : Paallelsm eos of the spndle to the efeence coodnate sstem E : Poston and otatonal devatons of spndles : Rotatonal angle of spndle : Machne postons along Z-as B : Length along the Z-as of the bong ba R T : Radal poston of tool tp aganst the bong ba as E : Dstance between O T and O E of the tool tp along the Y-as : Dstance between O T and O E of the tool tp along the Z-as E In the pesent eseach, t s assumed that the paallelsm eos and the squaeness eos ae eo, n ode to smplf the analss. s egads to the knematc moton devatons, E and E ae gven n the followng equatons. C C E 3-3 E

53 - 4 - whee, : ngula poston devaton of -as n spndle as C : ngula poston devaton of Y-as n spndle as C C : Postonng devaton of -as n spndle as C C : Postonng devaton of Y-as n spndle as C E 3-4 whee,, : Postonng devatons,,, : Staghtness devatons In the pesent eseach, t s assumed that the postonng eos and the staghtness eos n -as ae eo, snce the motons n the -as ae fed n the bong pocesses Fomulaton of knematc motons n bong pocesses Spndle moton The spndle moton s epesented b the followng equaton. E E RS _ actual RS C sn C cos cos sn cos sn C sn C cos sn cos sn cos C C cos sn sn cos Bong ba moton The moton of bong ba s epesented b the followng equaton. [ ] 5. 3 Eq B 3 SB _ actual SB E

54 - 4 - f cos sn cos sn f sn cos sn cos B 3-6 whee, sn cos C sn C cos f sn cos C sn C cos f B B Tool tp moton The moton of the tool tps ae epesented b the followng equaton based on Eq [ ] R 6. 3 Eq T BT_actual BT R f cos sn cos sn f sn cos sn cos B T whee, sn cos cos R C sn C cos f sn cos sn R C sn C cos f B T 4 B T Fomulaton of knematc motons of cuttng edge n bong pocesses Genealed geometc models of nseted cuttes have been poposed b Kamakc et al. usng mathematcal modelng. n appoach smla to that of Engn and ltntas has been used contanng cetan modfcatons and mpovements. Fstl, usng the nputs, a mathematcal model of one nset was developed on the local coodnate sstem postoned at the cuttng efeence pont of the nset. Fgue 3- llustates the local coodnate sstem and the cuttng efeence pont on two dffeent nsets. The am of ths model s to calculate the contol ponts that ae suffcent to defne the featues nose adus, cone chamfe, wpe edge etc. on an nset Kamakc, 9. Thee ae vaous nseted tool tp geometes that can be used n the cuttng tools, and seventeen nseted tool tp shapes ae defned n ISO 3399 standads ISO 3399:6. The genealed geometc model of the nseted tools s shown n Fg. 3-, statng wth the placement of the tool tps on the cutte bodes, the dentfcaton of oblque tool angles needed n the cuttng mechancs model and the knematcs of cuttng opeatons. The geomet of the tool tps ae defned n the local coodnate sstem O T analtcall.

55 Fg. 3- Cuttng efeence ponts on dffeent nsets Kamakc, 9 w Z T O T Y T κ L E e Z E O E Y E E CRP Fg. 3- Tool tps and cuttng edges of bong pocesses dapted fom Kamakc, et al., The contol ponts ae deved as functons of nset paametes that have been adapted fom Kamakc et al.. The coodnates of the contol ponts ae gven as follows based on the standaded tool tp geometes. CRP,,,,,, B,,, b cotκ cscκ,, cotκ cscκ, e s e - 4 -

56 C,,, cotκ cscκ, e e D,, E,,, e, κ cosκ tan,e cscκ L cosκ cos κ csc b snκ - s e cosκ, L snκ csc sn κ b snκ cosκ s e O T,,, L cosκ cosκ wcos κ cos κ csc b snκ cosκ, L snκ w sn κ csc sn κ bs snκ e s e 3-8 whee, CRP : Cuttng efeence pont, B, C, D and E : Contol ponts of cuttng edge : Tool ncluded nose angle w : Inset wdth L : Inset length κ : Cuttng edge angle of the nset b s : Wpe edge length : Cone adus e Theefoe, the motons of the cuttng edge n tool tps ae epesented b the followng equaton based on Eq. 3-8 and multpled wth Eq TE _ actual E E 3 [ Eq. 3 7 ] TE E TE E Lcosκ wcos κ cos κ cscbs snκ cosκ L snκ w sn κ csc sn κ bs snκ cos κ cos sn cos sn f3 sn cos sn cos f4 E RT B E 3-9 TE_actual

57 The knematc motons of the cuttng edge of bong pocesses aganst the efeence coodnate sstem O R ae pesented b Eq. 3- ncludng the knematc devatons B T,Bong B 5 T 6 4 3,Bong B 5 T 6 4 3,Bong F F F F R P F F cos C sn cos R C cos F F F F P F F sn sn R C sn F F F F C cos P 3- whee, cos sn b F sn F sn F sn F cos sn cot Lcos b wcos F L sn F w sn F sn cos F sn cos F e s e s κ κ κ κ κ κ κ κ κ κ 3.5 Knematc Moton Devatons n Tunng Pocesses 3.5. Shape geneaton motons n tunng pocesses The tunng pocesses on CNC tunng centes ae caed out b the spndle otatons, the lnea feed moton along the Z-as and depth of cut along the -as. Theefoe, the moton devatons of the spndle otaton ae an mpotant ssue fo evaluatng the geometc devatons of tuned pats. S catesan coodnate sstems shown n Fg. 3- ae set to epesent the knematc moton devatons whch ae n accodance wth Fg The ae O R, O S, O CR, O CS, O T and O E whch epesent the coodnate sstems of the efeence, spndles, caages, coss sldes, tool tps and cuttng edges, espectvel.

58 RS RCR CRCS CST TE Fg. 3- Coodnate sstems and the devatons of tunng pocesses The shape geneaton pocesses of the machne tools ae geneall epesented b the shape geneaton motons, and also the tool geometes. The shape geneaton motons, whch ae the elatve motons of the tools aganst the wokpeces, ae eecuted b a set of gd component of the machne tools Sugmua and Muabe, 997. The shape geneaton motons of the cuttng edge aganst the efeence ae descbed b Eq. 3-. S RS - RCR CRCS CST TE E 3- The ndvdual matces nclude some knematc and poston devatons due to both the moton eos and the set-up eos, theefoe, the knematc moton devatons n the tunng pocesses ae dscussed n the followng equaton s obtaned fom Eq. 3- b applng the paametes mentoned above S E RS E RS RCR E ECRCS CRCS E CST L CST L TE E TE E E 3- whee, E : Postonng devatons and staghtness devatons n Z-as E RS : Paallelsm eos of the spndle to the efeence coodnate sstem E : Poston and otatonal devatons of spndles : Rotatonal angle of spndle : Machne postons along Z-as B : Length along the Z-as of the bong ba R T : Radal poston of tool tp aganst the bong ba as E : Dstance between O T and O E of the tool tp along the Y-as : Dstance between O T and O E of the tool tp along the Z-as E The tems mentoned above ae needs n Eq. 3- as Eq. 3- : Machne postons along -as E : Dstance between O T and O E of the tool tp along the -as L, L : Dstance between O CS and O T E : Postonng devatons and staghtness devatons n -as E CRCS : Squaeness eos between the Z-as and -as

59 In the pesent eseach, t s assumed that the paallelsm eos and the squaeness eos ae eo, n ode to smplf the analss. s egads to the knematc moton devatons, E and E ae gven n the followng equatons. 3-3 whee, : ngula poston devaton of -as n spndle as C : ngula poston devaton of Y-as n spndle as C C : Postonng devaton of -as n spndle as C C : Postonng devaton of Y-as n spndle as C E 3-4 whee,, : Postonng devatons,,, : Staghtness devatons. In the pesent eseach, t s assumed that the postonng eos and the staghtness eos n -as ae eo, snce the motons n the -as ae fed n the tunng pocesses Fomulaton of knematc motons n tunng pocesses Spndle moton The spndle moton s epesented b the followng equaton. RS _ actual RS - 6 E cos sn sn cos C C E C C E

60 cos sn sn cos C cos sn C sn cos Caages moton The motons of caages ae epesented b the followng equaton. [ ] 3 RCR RCR_actual 5 3. Eq E g cos sn sn cos g cos sn g sn cos whee, sn cos sn cos g sn C cos g sn C cos g Coss sldes moton The moton of the coss sldes ae epesented b the followng equaton based on Eq [ ] 6 3 Eq. CRCS l CRCS_actua sn cos g cos sn sn cos sn g cos sn cos g sn cos Tool tps moton The moton of the tool tps ae epesented b the followng equaton based on Eq [ ] L L 7 3. Eq 3 CST CST _ actual CST g g cos sn sn cos g g cos sn g g sn cos

61 whee, g cos g g L cos L L sn sn L cos sn L cos sn L Fomulaton of knematc motons of cuttng edge n tunng pocesses Fomulaton of knematc motons of cuttng edge n tunng pocesses use fomulae smla to those used n bong pocesses. The genealed geometc model of the nseted tool n tunng pocesses s shown n Fg. 3-3, whch ae pesented statng wth the placement of the tool tps on the cutte bodes, the dentfcaton of oblque tool angles needed n the cuttng mechancs model and the knematcs of cuttng opeatons. The geomet of the tool tps ae defned n the local coodnate sstem O T analtcall. The contol ponts ae deved as functons of nset paametes that have been adapted fom Kamakc et al.. The coodnates of the contol ponts ae gven as follows based on the standaded tool tp geometes. CRP,,,,,, B,, C,, D,, E,, O T,,,, b,, cot κ csc κ,, cot κ csc κ csc κ,, cot κ csc κ cosκ,, cos κ csc b κ cosκ tan L snκ csc sn κ b snκ cosκ,, L cosκ cos κ csc b snκ - cosκ L snκ w sn κ csc sn κ bs snκ e e e e e s e e s L cosκ w cos κ snκ cos κ e s s e e

62 w T L E κ e O T Z T E O E Z E E Fg. 3-3 Tool tps and cuttng edges of tunng pocesses dapted fom Kamakc, et al., The motons of the cuttng edge n tool tps ae epesented b the followng equaton based on Eq. 3-9 and multpled wth Eq TE _ actual 3 [ Eq. 3 8 ] TE E TE E E L snκ w sn κ csc sn κ bs snκ cosκ E Lcosκ wcos κ cos κ cscbs snκ cosκ cos sn g g4 E sn cos g g5 TE_actual cos sn sn cos g3 g6 E 3-3 The knematc motons of the cuttng edge of tunng pocesses aganst the efeence coodnate sstem O R ae pesented b Eq. 3-3 ncludng the knematc devatons. P P P,Tunng,Tunng,Tunng cos G C L cos sn cos cos G L 3 s G C cos sn L sn sn sn G L L b G G G G G G G cos sn L G G

63 whee, G cos sn G G 3 w sn κ L snκ G 6 b G s 7 G 5 G 4 sn κ G sn 8 G 4 cos κ G sn 8 G G 5 7 e cotκ ; sn κ Lcosκ ; G 8 G w cos κ b snκ cosκ s 6 e 3.6 Vtual Machnng Sstems 3.6. Vtual machnng sstems fo bong and tunng pocesses The vtual machnng sstems have been developed to smulate the bong and tunng pocesses, and a set of ponts ae analtcall geneated to epesent the boed and tuned faces ncludng the knematc devatons. Fgue 3-4 llustates the pocedue of the vtual bong and tunng pocesses based on the nput data of the knematc devatons, the nseted tool tp paametes and the cuttng condtons f, v c, a p and t w ae feed ate, cuttng speeds, depth of cut and lengths of boed holes and tuned pats, espectvel. The geneaton and estmaton of the poston of cuttng edges wth knematc devatons aganst the efeence coodnate sstem ae caed out base on Eq. 3- fo bong pocesses and Eq. 3-3 fo tunng pocesses. These can be tansfomed nto the fnal tool poston b ncopoatng the geometc eo paametes, whch ae gven andoml based on the nomal dstbutons. Once the postons of the cuttng edges ae obtaned, the net step s to geneate all ponts on the geneated faces of the wokpeces. The cuttng edges of the sngle pont cuttng tool has a nose adus; theefoe, the contact ponts of the cuttng edges and the wokpeces can be descbed n the coss sectonal plane epesented b the YZ-plane fo bong pocesses and the Z-plane fo tunng pocesses as shown n Fg The ctcal tool angles ae estmated fo epesentng the etent of the tool nose, whch geneate the machned face. When the knematc devatons ae consdeed, the tool nose centes ae no longe on a staght lne, and the etents of the tool nose also changes contnuousl. Unde these condtons, the dsceted tool nose adus can then be epesented and evaluated

64 B, R T,,L, L κ, w,,e,bs,l κ, w,,e,bs, L f,v c,a p,t w f,v c,a p,t w a Bong pocesses b Tunng pocesses Fg. 3-4 Flow chat fo smulatons of the bong and tunng pocesses P nt P nt Y C φ j e h P md e b a φj je φ C h e P md φ j a b C Z feed feed a Bong pocesses - 5 -

65 feed feed C b φ j e P md h Pnt a C φ j e a φj e P nt P md h e b φ j C Z b Tunng pocesses Fg. 3-5 Detemnaton of goove se fomed b tool nose geomet wth knematc devatons dapted fom Ramaswam, In Fg. 3-5, C -, C and C ae the tool nose cente locatons at thee consecutve evolutons of the spndle, e s the coespondng tool nose adus, and P nt-, P nt ae the ntesecton pont and the tool contact angle φ j- and φ j. Based on the locatons of the tool nose centes fo thee consecutve evolutons at the same angula poston of the spndle, based on the contact angle φ j- and φ j of the tool nose dung the second evoluton can be calculated and the tool nose can be dsceted. The coodnates of the ntesecton pont P nt- and P nt of the tool nose pofles between the tool nose locatons C -, C and C can be calculated as follows that have been adapted fom Ramaswam : In tangles P nt- P md- C - and P nt- P md- C, a h ; e b h e ; Let a b d ; a P Y Z md nt nt d d Y Z C ;h a md md h h C d e Z d Y d a C Z Y ;

66 In tangles P nt P md C and P nt P md C can be calculated smlal wth the tangles P nt- P md- C - and P nt- P md- C. The stat and end contact angles of the tool nose wth the wokpece can be calculated b the followng equatons that have been adapted fom Ramaswam : In tangles P nt- P md- C, Eq s obtaned. Pnt C CC φ j cos 3-33 Pnt C CC In tangles P nt P md C, Eq s obtaned. Pnt C C C φ j cos 3-34 Pnt C C C t an gven tool nose locatons elated to the angula oentaton of the spndle wth espect to the efeence oentaton, the span of the tool contact angle between the stat and end angle can be dvded as equed. The pofle of the machned face can then be geneated as a functon of the fnal poston of the cuttng edges consdeng all knematc devatons [ ''', ''', '''], whee, ''', ''', ''' ae the geometc devatons of poston n the, Y and Z-as, obtaned fom the knematc moton devatons of both the spndle and the Z-as feed motons. The tool nose adus e and the tool contact angle φ j b applng the followng equaton. Ft f ; R nst π R R cosφ Y Z suf _ bong suf _ bong Y Z suf _ bong suf _ tunng suf _ tunng suf _ tunng d nst e j R R cosφ t d nst F cosφ e e j j Rd Rnst e secφj R R secφ F t d nst e e cosφ j j sn cos sn cos whee, suf_bong, Y suf_bong, Z suf_bong suf_tunng, Y suf_tunng, Z suf_tunng : Postons of a pont on the boed faces : Postons of a pont on the tuned faces

67 R d R nst f : Radus of boed and tuned faces : Instantaneous adal dstance of the tool nose cente fom the pat as : The feed ate pe evoluton. B epeatng ths pocess at each locaton of the tool, the ente suface of the machned pat can be ceated. Net secton llustates sample boed holes and tuned pats geneated usng the vtual machnng module Smulaton of 3-dmensonal boed and tuned faces Ths secton shows an eample of the geneated faces b bong and tunng pocess smulatons consdeng knematc devatons. s shown n the fgue, a set of the ponts on the boed and tuned faces ae geneated. The geometc devatons of an ponts on the boed and tuned faces can be evaluated b compang the geneated faces wth the knematc devatons. In ode to valdate the vtual machnng module of bong and tunng pocesses, two pats ae consdeed between the boed and tuned faces wthout knematc devatons and anothe one wth knematc devatons Smulaton of boed and tuned faces wthout knematc devatons Fgues 3-6 and 3-7 show the smulaton of the vtual machnng of the boed and tuned faces wthout knematc devatons, whch s smulated b pogam MTLB n ode to show the dscepanc of the machned and nomnal sufaces. The smulatons of the bong and tunng pocesses ae caed out based on Eq and 3-36, espectvel. The machnng paametes of bong and tunng pocesses conssts the nput data ae descbed as follows: Machnng paametes fo bong pocesses, f.5 mm/ev, 3 mm, B 73 mm, R T mm, e.8 mm; κ, 8, w 6.35 mm, b s mm, L 6.35 mm. Machnng paametes fo tunng pocesses, f.5 mm/ev, 3 mm, 35 mm, L mm, L 5 mm, R d mm, e.8 mm, κ, 8, w 6.35 mm, b s mm, L 6.35 mm. 3 ll the knematc moton devatons ae set to be eo. The boed and tuned faces ae obtaned fom 8, ponts geneated b the bong and tunng pocess smulatons n the Fgs. 3-6 and 3-7. The geneated sufaces ae ve smooth and onl have the dstances due to the nose adus n the tool geometes and the feed ates n the machnng paametes

68 Fg. 3-6 Estmated geometes of boed faces wthout knematc moton devatons Fg. 3-7 Estmated geometes of tuned faces wthout knematc moton devatons

69 3.6.. Smulaton of boed and tuned faces wth knematc devatons Fgues 3-8 and 3-9 show the smulaton of the vtual machnng of the boed and tuned faces wth knematc devatons whch s the smulaton method smla to the method of Fgs. 3-6 and 3-7, but the nput data of geometc devaton eos ae dffeence. The machnng paametes of bong and tunng pocesses conssts the nput data ae descbed as follows: Fgues 3-8 and 3-9 show the smulaton of the vtual machnng of the boed and tuned faces wth knematc devatons. The machnng paametes ae same as ones fo the smulatons wthout knematc moton devatons shown n the pevous secton. The knematc moton devatons ae set as shown n the followngs. Poston devatons of spndles C and C n Eqs. 3-3 and 3-3 ae gven andoml based on the nomal dstbuton N, µm along the spndle otaton, Rotatonal devatons of spndles and n Eqs. 3-3 and 3-3 ae gven andoml based on the nomal dstbuton N, 3 µad along the spndle otaton, 3 Postonng devatons n Z-as n Eqs. 3-4 and 3-4 ae gven andoml based on the nomal dstbuton N, 5 µm along the Z-as feed moton, 4 Staghtness devatons n Z-as and n Eqs. 3-4 and 3-4 ae gven andoml based on the nomal dstbuton N, µm along the Z-as feed moton, and 5 Postonng and staghtness devatons n -as n Eqs. 3-4 and 3-4 ae set to be, snce the -as ae fed n both the bong and the tunng pocesses. Fg. 3-8 Estmated geometes of boed faces wth knematc moton devatons

70 Fg. 3-9 Estmated geometes of boed faces wth knematc moton devatons Fgues 3-8 and 3-9 show the eamples of the machned sufaces obtaned fom 8, ponts geneated b the bong and tunng pocess smulatons. The geneated sufaces have lage dstubances compaed wth the ones shown n Fgs. 3-6 and 3-7. The dstubances ae due to the knematc moton devatons of the spndle and the Z-as table. 3.7 Concluson The eseach dscussed n ths chapte deals wth the vtual machnng of bong and tunng pocesses ncludng knematc moton devatons. smulaton model fo the bong and tunng pocesses s poposed to evaluate the geometc devatons of the geneated faces. The followngs ae concluded. model s poposed to epesent the knematc motons of the cuttng edges aganst the wokpeces fed on the spndles, takng nto consdeaton of the knematc devatons of the bong tool sstems of the machnng centes and tunng tool sstems of the tunng centes. The models poposed hee epesent the postons of the cuttng edges aganst the wokpces b applng the 4 b 4 tansfomaton matces ncludng the knematc moton devatons. sstematc method s poposed to estmate the geometc devatons of the machned face based on the knematc motons of the cuttng edges. set of ponts on the boed and the tuned faces ae geneated b applng the poposed method and the chaactestcs featues of the geneated faces ae estmated based on the ponts

71 3 poposed model and method ae appled to the smulaton of the smple bong and tunng pocesses. The geometes of the boed and tuned faces ae estmated, based on the cuttng condtons, the tool geometes and the knematc devatons of the bong and tunng pocesses

72 Chapte 4 Estmaton of 3-Dmensonal Suface Roughness Includng Knematc Moton Devatons

73 4. Estmaton of 3-Dmensonal Suface Roughness Includng Knematc Moton Devatons 4. Intoducton In the pesent global compettve stuaton, manufactung pocesses n ndust ae developng contnuousl to ncease the qualt and the elablt of the poducts and to decease the cost of the manufactung pocess opeatons. In geneal t s poblematc to detemne the values of the pocess paametes n pactce and to mame the manufactung sstem pefomance usng the avalable esouces. The suface fnsh of the machned pats s one of the most mpotant poduct qualt chaactestcs. Suface oughness geatl nfluences the mechancal and phscal popetes of the contactng pats. The undestandng of the behavo s mpotant n man applcatons such as wea, fcton, lubcaton, sealng tghtness of jont, contact gdt, contact stess, loaded aea and themal conductvt. Theefoe, engnees ae ve concened about the suface oughness of the poducts Dong, et al., 99. Fg. 4- Ke components of estmaton of the 3D suface oughness The development of new ndustes has led to a equement fo supe-smooth sufaces and fo the ablt to measue and pedct sufaces oughness of ndustal pats befoe eal machnng pocesses. The estmaton of 3-dmensonal 3D suface oughness of machned pats befoe eal machnng pocess s mpotant fo the desgn and the manufactung pocess of poducts. The - 6 -

74 smulaton of vtual machnng s one method of estmatng the 3D suface oughness fom vtuale pats of machnng pocesses. Ths secton dscusses the 3D suface oughness that can be estmated fo the vtual pat pofles as shown n Fg. 4-. The ke components of estmaton of 3D suface oughness based on smulaton of vtual machnng module n ths chapte ae: Refeence datum fo clnde assessment Mathematcal models of least mean squaes Fomulaton fo estmaton of the suface oughness Case Stud Detals of these models ae povded below: 4. Refeence Datum fo Clnde ssessment In ecent eas, the assessment of 3D suface oughness has become moe and moe popula n both academa and ndustes. Howeve t would seem that the choce of sutable efeence planes s stll dscetona and abta. lthough some efeence planes have alead been etended fom efeence lnes and appled to 3D topogaph chaacteaton, lttle nfomaton s avalable on the elatve effcenc and feasblt of the efeence planes, especall fo those used fo nomnall cuved sufaces. Fom a standadaton pont of vew ths causes two poblems. The fst s that t s dffcult fo uses to detemne what efeence planes to use and the second s that t s dffcult to ca out a compason between measuement esults whch ae obtaned b usng dffeent efeence planes Dong, et al., 995. In ode to be able to fnd a sutable efeence datum fo 3D topogaph chaacteaton, ths secton stats wth assessment clnde of the measuement of fom devatons. Measuements of fom devatons of engneeng components ae caed out wth espect to a efeence datum o tajecto. Fo eample, staghtness measuements ae caed out wth efeence to a staght edge and oundness measuements wth efeence to a ccula tajecto. The devatons have to be measued aganst the nomnal geometc elements. ISO specfes that the actual measuement such that mamum devaton between the datum and the actual featues concened s the least mean squaes fo evaluatng the fom eos Shunmugam, 987. The assessment clndes shown n Fg. 4- ae consdeed hee as the efeence datum to measue the 3D suface oughness of boed and tuned sufaces. The assessment clndes ae geneated based on all the 3D coodnate data geneated b the 3D bong and tunng pocess smulatons

75 e Z R,, a l,b m, R ϕ a O α R E β b O P, Y, Z ψ Y R Y R a Coodnate sstem fo clnde P,Y,Z R E O b O α R a b Detals of data on Y plane Fg. 4- Coodnate sstem fo measung devatons pocedue s poposed to geneate an assessment clnde n ode to vef the 3D suface oughness based on all the tajectoes of the cuttng edge n the bong and tunng pocesses. The paametes to be detemned hee ae summaed n the followng, whch epesent a clnde n the efeence coodnate sstem R Y R Z R

76 Unt vecto l, m, n epesentng the decton of the as of the assessment clnde, Vecto a, b, epesentng the poston of the as of the assessment clnde, 3 R epesentng the adus of the assessment clnde, 4 E epesentng the devaton of th pont espect to the least mean squae clndes, 5, Y, Z epesentng the Catesan coodnates of th pont, 6 epesentng the adus vecto of Catesan coodnate of th pont, gven as Y, 7 epesentng the angula coodnate of Catesan coodnate of th pont, 8 e epesentng the eccentct gven as e a b, 9 α, β epesentng the angula coodnate of -as and Y-as, espectvel, ϕ, ψ epesentng the otatonal angle aound -as and Y-as, espectvel. 4.3 Mathematcal Models of Least Mean Squaes 4.3. Devaton of least mean squaes Thomas and Chan, 989 The efeence coodnate sstem R Y R Z R concdes the one n Fg. 3-7 fo bong pocesses and Fg. 3-8 fo tunng pocesses, theefoe, the paametes l and m ae fed, the paametes a, b, and R ae estmated b applng the followng equatons, based on the least mean squae method poposed b Thomas and Chan 989. Gven a set of coodnate, Y, Y N, Y N, defne a ccle wth cente a, b and adus R. We defne the eo as the dffeence between the constant aea πr and the aea of the ccle centeed at a, b and has adus [ a Y b ] /. f Summng up the squaes of the eos we have R [ π R { a Y b }] N,a,b π o J f π N [ R { a Y b }]. 4- The functon JR, a, b should be mnmed wth espect to R, a and b. Dffeentatng Eq. 4- wth espect to R elds

77 { } [ ] N R b Y a R R J o { }. b Y a NR N 4- Dffeentatng Eq. 4- wth espect to a elds { } [ ] N a b Y a R a J o { } [ ] { } [ ] a b Y a R b Y a R N N snce RHS ght hand sde s eo fom Eq. 4-. Theefoe, { }. b Y a R N N 4-3 Smlal dffeentatng Eq. 4- wth espect to b elds { }. Y b Y a Y R N N 4-4 Equatons 4-, Eq. 4-3 and Eq. 4-4 can be solved, even though quadatc, usng the followng tcks. Fst, let us smplf the notatons usng the followng conventons. We use summaton ove n ndces as and let stand fo N and Y Y Y Y Y Y Y Y Y Y. Y Y Wth these conventons, Eq. 4- becomes

78 Nb b Na a NR Y Y 4-5 and Eq. 4-3 becomes Y Y 3 b b a a R 4-6 and Eq. 4-4 becomes. b b a a R Y Y 3 Y Y Y Y Y 4-7 Equatons 4-5, 4-6 and 4-7 can be solved. Multpl Eq. 4-5 b and subtact N multpled b Eq. 4-6 to gve [ ] [ ] 3 Y Y Y Y N b N N a N 4-8 Multpl Eq. 4-5 b Y and subtact N multpled b Eq. 4-7 to gve [ ] [ ] 3 Y Y Y Y Y Y Y Y Y N b N N a N 4-9 We can now solve Eq. 4-8 and 4-9 fo a and b ; the esult can be wtten n mat fom as c c b a b a b a 4- whee,,, 3 3 Y Y Y Y Y Y Y Y Y Y Y Y Y N N c N N c, N b, b N a N b, N a

79 fom whch b a b a b c b c a 4- and. b a b a c a c a b 4- Havng solved a, b we can substtute nto Eq. 4-5 to get R, whee { } Nb b Na a N R Y Y 4-3 The least mean squae eos E of all the geneated pont P, Y, Z and the assessment clnde s gven n the followng equaton, as shown n Fg. 4-. Theefoe, the tansfomaton matces between the efeence coodnate sstem R Y R Z R and the local coodnate fo clnde ae gven as follows. Z Y b a cos sn sn cos cos sn sn cos R R R ϕ ϕ ϕ ϕ ψ ψ ψ ψ ϕ ψ ψ ϕ ψ ϕ ψ ψ ϕ ϕ ϕ ϕ ψ ψ ϕ ψ ϕ ψ ψ sn cos b sn a cos cos Z sn cos Y sn cos b sn Z cos Y sn sn b cos a cos sn Z sn sn Y cos R R R R R R R R 4-4 ssume ψ and ϕ, theefoe, Eq. 4-5 s obtaned. b Z Y a Z R R R R ϕ ψ b Y a Z R R R ϕ ψ 4-5

80 Gven l ψ and m -ϕ, theefoe, the Eq. 4-5 s used n the least mean squae eos E of all the geneated pont P, Y, Z and the assessment clnde s gven n the followng equaton. E lz a Y mz b R 4-6 The sum of the squaes of the devaton s as follows. N E s E lgothm fo calculatng paametes The pocedue fo calculatng paametes s shown n Fg. 4-3, all data ponts P, Y, Z ae geneated b the 3D bong and tunng pocess smulatons. The algothm fo calculatng paametes a, b, l, m and R of the assessment clndes ae estmated b applng the followng pocedue. STEP : Settng of paametes l and m The paametes l and m ae set n the ntal values -. and moved to. b the step of.. These paametes ae nput nto b applng the followng matces. m l m l R YR Z R 4-8 STEP : Estmaton of paametes a, b, and R The paametes a, b, and R ae estmated b applng the Eqs. 4- to 4-3 fo all the combnaton of l and m. STEP 3: Estmaton of least mean squae eos E s and select an optmal paametes. The least mean squae eos E s s calculated b applng Eq. 4-7 based on the paametes of a, b, l, m, R and the geneated ponts P, Y, Z. combnaton of the paamete values whch mnme E s s selected as the paametes epesentng the assessment clnde. The paametes a, b, l, m and R obtaned hee gve the poston and oentaton eos and the dmensonal eo n the adus of the boed and tuned clndes geneated b the smulatons

81 l m a,b, R E s a,b,l,m, R Fg. 4-3 Flowchat fo calculatng paametes of least mean squaes 4.4 Fomulaton fo Estmaton of the Suface Roughness 4.4. Two-dmensonal suface oughness Sufaces ae chaacteed b thee man paametes: oughness, wavness, and la. Roughness means the egulates of a suface, usuall esultng fom a poducton pocess o usage, such as machnng o wea. These egulates ae tpcall submcon n scale. Wavness descbes a moe wdel spaced component on the suface, wth lage dmensons; fo nstance, the devaton fom flatness. So, thnkng analogousl, wavness s a knd of cae wave and oughness s the modulaton ove t. La s defned as the man decton of the suface tetue. Ths s often detemned b the poducton method, such as the decton of gndng, tunng etc. These suface chaactestcs ae depcted schematcall n Fg. 4-4 Rantala, 4. Roughness s measued b contact poflomete-tpe devces that de on the suface on a skd-whch povdes the efeence fo the measuements o non-contact devces such as ntefeomet-based o, ecentl, atomc foce mcoscopes. The nstument used s dependent on the esoluton needed fo the measuement. Ths eseach does not dscuss these nstuments because the eseach focuses on estmated smulaton of vtual machnng

82 Fg. 4-4 Suface oughness temnolog dapted fom Kalpakjan and Schmd, 8; Rantala, 4 fte geneatng the assessment clndes, suface oughness s estmated as the theoetcal suface oughness of mamum heght R_th, the theoetcal suface oughness of athmetcal mean devaton Ra_th, the -dmensonal D suface oughness of mamum heght of the assessed pofle R, athmetcal mean devaton of the assessed pofle Ra and oot mean squae of the assessed pofle Rq defned n ISO 487:997 and JIS B 6: ae estmated b Eqs. 4-9 to 4-3. The fomulatons of the D suface oughness ae estmated b applng the followng Theoetcal suface oughness The dealed model fo the suface oughness usng a tool havng a nose adus e used n bong and tunng pocesses wth feed ate f s shown n Fg R_th, the suface oughness defned n JIS B 6:, can be estmated b the suface oughness show n Eq. 4-9, and Ra_th defned b Donfeld and Lee s shown n Eq. 4-. f R _ th e

83 e. 3 f Ra _ th 4- e f R _ th Fg. 4-5 Idealed model of D suface oughness JIS B 6: Mamum heght of the assessed pofle The D suface oughness of R s obtaned fom the dstance between the hghest peak and the lowest valle n the ange of sampled efeence length l n the decton of mean lne of the oughness cuve. fte geneatng the assessment clndes, the suface oughness paamete, R, can be estmated accodng to JIS B 6: b measung the lnes of.5 mm accodng to JIS B 633:, as shown b the fomula n Eq. 4-. { E } mn{ } R Rp Rv ma 4- E Fg. 4-6 Defnton of the R ampltude paametes JIS B 6: thmetcal mean devaton of the assessed pofle The D suface oughness of Ra defned n JIS B 6: s obtaned fom the followng fomula when the oughness cuve s epessed b f, takng -as to the mean lne decton and Y-as to the vetcal magnfcaton of the oughness cuve n the ange of sampled efeence length l. n ndcatve calculaton of Ra s shown n Fg. 4-7, 4-8 and Eq

84 Ra l l d a b c N... N N N E 4- Fg. 4-7 Defnton of the Ra ampltude paametes JIS B 6: Fg. 4-8 Coodnates used fo measuement of suface oughness Kalpakjan and Schmd, Root mean squae of the assessed pofle The D suface oughness of Rq defned n ISO 487:997 s obtaned fom the followng fomula when the oughness cuve s epessed b f, takng -as to the mean lne decton and Y-as to the vetcal magnfcaton of the oughness cuve n the ange of sampled efeence length l. n ndcatve calculaton of Rq s shown n Fg. 4-8 and Eq / / l N a b c... N d N N Rq l E /

85 4.4. Thee-dmensonal suface oughness Blateon, 3 Contnung fom geneatng the assessment clndes and estmatng the D suface oughness, the 3D suface oughness whch has not et been addessed wdel, should be consdeed. In the followng, a captal lette S fo Suface s used to dentf 3D paametes, n ode to dstngush D and 3D paametes accodng to ISO 578 pat. The 3D suface oughness was poposed b Dong et al. 994, Qunsat et al. 8 and bouelatta to assess the 3D suface topogaph based on the least mean squaes plans. The paametes of mamum heght of the suface S, n ths eseach has been adapted fom Blateon 3, and the athmetc mean heght of the suface Sa and oot mean squae heght of the suface Sq have been adapted fom bouelata, Dong et al. 994, Qunsat et al. 8. The 3D suface oughness paametes ae estmated b applng the followng equatons Samplng aea Pofle paametes ae defned based ethe on a samplng length o the evaluaton length. If a paamete s defned on a samplng length, t s b default calculated on each samplng length ISO 488:996 and a mean value calculated the default numbe of samplng lengths s fve. Wth sufaces and aeal paametes, the concepts of samplng and evaluaton aeas ae stll defned but the default s one samplng aea pe evaluaton aea. Ths smpl means that paametes ae calculated on the measued suface wthout segmentng the suface nto small subaeas that depend on the samplng length Blateon, Mamum heght of the Suface The 3D suface oughness paamete of mamum heght of the suface S has been smlal estmated wth the D suface oughness that s evaluated b measung the lnes of.5 mm, but 3D suface oughness s evaluated b measung the aeas.5 mm.5 mm squae fom the ponts of the geneated faces efeng to JIS B 633:. Fgue 4-9, the Sp paamete epesents the mamum peak heght, that s to sa the heght of the hghest pont of the suface. The Sv paamete epesents the mamum pt heght,.e. the heght of the lowest pont of the suface. s heghts ae counted fom the mean plane and ae sgned, Sp s alwas postve and Sv s alwas negatve Blateon, 3. Equaton 4-4 s sum of the mamum heght of the suface b applng the followng equatons. { E } mn{ } S Sp Sv ma 4-4 E - 7 -

86 Fg. 4-9 Defnton of S of the suface Mchgan Metolog, thmetc mean and oot mean squae heght of the suface The 3D suface oughness paamete of the athmetc mean of the suface Sa and oot mean squae heght of the suface Sq ae defned as the athmetc mean of the absolute value of the heght wthn a samplng aea and s epessed b, Blateon, 3. The paamete s evaluated b measung the aeas.5 mm.5 mm squae fom the ponts of the geneated faces efeng to JIS B 633: b applng the followng equatons. Sa, dd E N N 4-5 / N, dd E N Sq / Case Stud Ths secton shows an eample of faces geneated b bong and tunng pocess smulatons consdeng knematc devatons. s shown n Fgs. 3-6 to 3-9, a set of ponts on the boed and tuned faces ae geneated. The geometc devatons of an ponts on the boed and tuned faces can be evaluated b compang the geneated faces wth the knematc devatons. The suface oughness of the geneated faces ae summaed n Tables 4-, 4- and 4-3 based on the smulaton esults unde twelve dffeent machnng paametes of the feed ates and tool nose adus of the nseted tool tps. The D and 3D suface oughness s evaluated b measung the lnes of.5 mm length and the aeas.5 mm.5 mm squae efeng to JIS B 633:

87 In ode to valdate the vtual machnng module of bong and tunng pocesses, two pats ae consdeed between the boed and tuned faces wthout knematc devatons and anothe one wth knematc devatons Estmaton of boed and tuned faces wthout knematc devatons Table 4- shows the compasons between the theoetcal values of the D suface oughness calculated fom the feed ates and the nose adus, and the D and the 3D suface oughness obtaned though the smulatons shown n Fgs. 3-6 and 3-7. s egads the D suface oughness, the estmated values of Ra and R ae almost the same as the theoetcal values Ra_th and R_th. The estmated values ae obtaned fom, ponts geneated b the bong and tunng pocess smulatons. The pecentage of mamum dffeences between the esults of the theoetcal and estmated values s less than 5.84 % fo Ra and 7.4 % fo R. Table 4- Estmated D and 3D suface oughness of bong and tunng pocess smulatons wthout knematc devatons Test no. Suface Roughness wthout Knematc Moton Devatons Cuttng Condton Theoetcal Smulatons Nomnal R_th Ra_th R [µm] Ra [µm] Rq S Sa Sq f e Damete [µm] [µm] Pedct Dff. % Pedct Dff. % [µm] [µm] [µm] [µm] [mm] [mm/ev] [mm] a b c a-c d b-d

88 4.5. Estmaton of boed and tuned faces wth knematc devatons Ths secton shows the estmaton of D and 3D suface oughness based on smulaton of the vtual machnng of the boed and tuned faces wth knematc devatons. The machnng paametes ae same as those used fo the smulatons wth knematc moton devatons shown n the pevous chapte. Table 4- Estmated D and 3D suface oughness of bong pocess smulatons wth knematc devatons Test no. Nomnal Damete Cuttng Condton Suface Roughness wth Knematc Moton Devatons Theoetcal Smulatons f e R_th Ra_th R Ra Rq S Sa Sq [mm] [mm/ev] [mm] [µm] [µm] [µm] [µm] [µm] [µm] [µm] [µm] Tables 4- and 4-3 summae the D suface oughness R_th, Ra_th, R, Ra and Rq, the 3D suface oughness S, Sa and Sq obtaned fom the bong and tunng pocess smulatons unde the vaous condtons of the feed ate f and the nose adus of the cuttng edges e. The obtaned suface oughness s much geate than the theoetcal values and also the smulaton esults shown n Table 4- due to the knematc moton devatons. The evaluated suface oughness s not so affected b the feed ate f and the nose adus e as the case of the smulaton wthout knematc moton devatons. Ths means that effects of the knematc moton devatons ae

89 geate than the effects of the machnng paametes. The estmated values ae obtaned fom, ponts geneated b the bong and tunng pocess smulatons. Table 4-3 Estmated D and 3D suface oughness of tunng pocess smulatons wth knematc devatons Test no. Nomnal Damete Cuttng Condton Suface Roughness wth Knematc Moton Devatons Theoetcal Smulatons f e R_th Ra_th R Ra Rq S Sa Sq [mm] [mm/ev] [mm] [µm] [µm] [µm] [µm] [µm] [µm] [µm] [µm] The values of 3D suface oughness of S geneall gve lage values than D suface oughness n most cases b the machnng condtons of f. mm/ev and e.8 mm fo bong pocesses, and of f.5 mm/ev and e. mm fo tunng pocesses. The Sa and Sq ae the smallest value of the suface oughness fo bong pocesses, as obtaned b the machnng condtons of f. mm/ev and e.6 mm, and fo tunng pocesses as obtaned b the machnng condtons of f. mm/ev and e. mm. The knematc moton devatons ae set as shown below. Poston devatons of spndles C and C n Eq. 3-3 and 3-3 ae gven andoml based on the nomal dstbuton N, µm along the spndle otaton, Rotatonal devatons of spndles and n Eq. 3-3 and 3-3 ae gven andoml based on the nomal dstbuton N, 3 µad along the spndle otaton,

90 3 Postonng devatons n Z-as n Eq. 3-4 and 3-4 ae gven andoml based on the nomal dstbuton N, 5 µm along the Z-as feed moton, 4 Staghtness devatons n Z-as and n Eq. 3-4 and 3-4 ae gven andoml based on the nomal dstbuton N, µm along the Z-as feed moton, and 5 Postonng and staghtness devatons n -as n Eq. 3-4 and 3-4 ae set to be, snce the -as ae fed n both the bong and the tunng pocesses. Fg. 4- D oughness pofle s evaluated b measung the lnes fo boed faces Fg. 4-3D suface oughness s evaluated b measung the aeas fo boed faces

91 Fg. 4- D oughness pofle s evaluated b measung the lnes fo tuned faces Length of tuned faces mm Fg D suface oughness s evaluated b measung the aeas fo tuned faces Fgue 4- and 4- shows the smallest value of Sa and Sq suface oughness fom Table 4- of the D oughness pofle whch s evaluated b measung the lnes fo boed faces, and 3D suface oughness s evaluated b measung the aeas fo boed faces. The estmated values ae used fo the machnng condtons of f. mm/ev and e.6 mm