Enginee ing Science and Technology, an In e na ional Jou nal 55 (2024) 101757
A ailable online 3 July 2024
2215-0986/© 2024 Ka abuk Uni e si y. Publishing se ices by Else ie B.V. This is an open access a icle unde he CC BY-NC-ND license
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Topog aphy simula ion o ee- o m su ace ball-end milling h ough
pa ial disc e iza ion o linea ised oolpa hs
Felipe Ma in
a
,
*
, Ad iano Fagali de Souza
b
, Hel on da Sil a Gaspa
c
, Amaia Calleja-Ochoa
a
,
Luis No be o L´
opez de Lacalle
a
a
Ae onau ics Ad anced Manu ac u ing Cen e (CFAA), Uni e si y o he Basque Coun y (EHU/UPV), Bilbao, Spain
b
Fede al Uni e si y o San a Ca a ina (UFSC), Flo ian´
opolis, B azil
c
Fede al Uni e si y o San a Ca a ina (UFSC), Join ille, B azil
ARTICLE INFO
Keywo ds:
F ee- o m
5-axis milling
Ball-end milling
API
CAD
CAM
ABSTRACT
F ee- o m su aces a e commonly p esen in se e al enginee ing componen s, om molds o mo e sophis ica ed
componen s o ae onau ical engines. These pa s a e usually inished by machining, mo e speci ically, ball-end
milling. In his p ocess, he con ac be ween he ool and he pa cons an ly changes along he oolpa h, esul ing
in se e al manu ac u ing p oblems ha damage he su ace and comp omise he pe o mance o he pa . Besides
he o dina y cu ing pa ame e s, hese machined su aces a e deeply in luenced by he ool ip cen e and he
elas oplas ic de o ma ion o he ma e ial h ough he shea ing and plowing pai . Knowing he exac o ien a ion
o he ool in ela ion o he su ace de e mines all aspec s o he milling p ocess and is necessa y o p ocess
modeling. The cu en CAD/CAM so wa e pla o ms is no able o p edic such su ace opog aphy. In his di-
ec ion, he cu en wo k p esen s a so wa e ou ine de eloped and implemen ed on an open in e ace CAD/
CAM so wa e (Siemens® NX). The no mal ec o s o he su ace o be machined, he cu e con ac (CC), and
cu ing loca ion (CL) da a om he oolpa h calcula ed by he CAD/CAM we e used o ob ain a comple e dis-
c e iza ion o he cu e -wo kpiece posi ion along he oolpa h. This in o ma ion was used o p edic he su ace
opog aphy and iden i y he cu ing-edge elemen s. Then, he de eloped model was used o e alua e he ee-
o m su ace o a blade milled on 5-axis oge he wi h con ocal imaging analysis. The esul s show ha he
me hodology de eloped can p edic he opog aphy aspec s o a ee- o m machined su ace and suppo he
analysis o milling p oblems such as un-ou .
1. In oduc ion
F ee- om su aces a e commonly p esen in se e al enginee ing
componen s, om dies and ools o mo e sophis ica ed componen s o
ene gy and ae onau ic indus ies. Du ing he manu ac u ing p ocess o
such pa s, ball-end ool ips a e ecommended, which can be di ec ly
applied on he su ace inish o indi ec ly o manu ac u ing ools and
consumables like elec odes o elec ical discha ge machining (EDM).
Such ools allow di e en con ac s o p oduce a ee- o m and smoo h
su ace. Howe e , due o he geome y o he ool ip, i p oduces c es
wa es ha signi ican ly inc ease he oughness o he machined su ace,
which can comp omise pe o mance and mus be e alua ed ca e ully.
In he design o u bines and ae onau ical engines, he shape o he
su ace o blades, impelle s, and blade-in eg a ed disks (BLISKs) can be
op imized o imp o e he ae odynamic low. This esul s in complex
shape designs, wi h ins an aneous adius changes o e he su ace ha
make he manu ac u ing p ocess challenging. Besides, such pa s usually
equi e high s eng h, wea , and he mal esis ance, demanding ha d- o-
cu ma e ials and inc easing design and machining complexi ies.
The aspec o he su ace gene a ed by he milling p ocess signi i-
can ly impac s he su ace in eg i y and pe o mance, being he mos
impo an ea u e o complex high-pe o mance pa s [1]. In blades and
ae o oiled componen s, o m e o s and o he milling p ocess signa u es
can conside ably educe he componen ’s pe o mance; hus, igh
design ole ances a e applied o enhance i s ene ge ic e iciency. Su ace
in eg i y also plays an impo an aspec in he a igue li e o c i ical
pa s, and o his eason, i has been ex ensi ely in es iga ed in he las
decades [2].
5-axis milling is p e e able o inish such pa s wi h ee- o m
geome ical shapes. I allows wide ool access, manu ac u ing
* Co esponding au ho .
E-mail add ess: [email p o ec ed] (F. Ma in).
Con en s lis s a ailable a ScienceDi ec
Enginee ing Science and Technology,
an In e na ional Jou nal
jou nal homepage: www.else ie .com/loca e/jes ch
h ps://doi.o g/10.1016/j.jes ch.2024.101757
Recei ed 1 Decembe 2023; Recei ed in e ised o m 18 Ap il 2024; Accep ed 28 June 2024
Enginee ing Science and Technology, an In e na ional Jou nal 55 (2024) 101757
2
geome ies ha would be di icul o impossible o p oduce wi h adi-
ional 3-axis due o gouging. Fu he mo e, i allows modi ica ion o he
ool’s o ien a ion and chip hickness o p oduce smoo he oolpa hs,
educing he oscilla ion o he cu ing o ces and o he ela ed p oblems
[3–5]. Also, i educes he numbe o se ups, imp o ing lead imes and
cos s.
To gua an ee he posi ion o he ool in 5-axis milling, ad anced NC
con olle s a e equi ed oge he wi h CAM so wa e capable o de el-
oping alid and op imized ool ajec o ies. In his p ocess, he ole ance
band mus be ca e ully adjus ed o main ain he pe o mance wi h a
leas a minimum su ace quali y. As he ole ance band educes, mo e
da a mus be p ocessed, and i can sa u a e he machine’s con ol loop,
esul ing in ins an aneous educ ions o p ocess pauses ha se e ely
damage he su ace [6]. Also, he da a dis ibu ion (CL poin s) inside he
ole ance band a ies acco ding o he so wa e house, mainly because
o di e en ma hema ical models used, esul ing in di e en pe o -
mances o each so wa e in he same machine [7]. Thus, he e alua ion
o he p ocess commonly conside s su ace e o s and machining ime
[8].
The opog aphic aspec o he milled su ace using he ball-end
ool ip on 5-axis milling can be es ima ed using di e en geome ical
models ha conside he ool posi ion in he space, i s diame e , he eed
pe oo h, he s epo e , and he ool un-ou . When ool un-ou is p e-
sen , one cusp emo es mo e ma e ial, causing di e en pa e ns on he
su ace [9]. The heo e ical su ace is ob ained by compu ing he
engagemen be ween he pa and piece, which is an impo an b anch
o su ace e alua ion and p edic ion. Mo eo e , geome ical models a e
equi ed in o ce p edic ion, de lec ion, and o m e o s. Fo hese ea-
sons, i has been ex ensi ely in es iga ed in he las decades [10].
Random su ace pa e ns indica e mo e complex p oblems ela ed o
ib a ion, p ocess cinema ics, wea , de o ma ions, o clamping issues
and mus be add essed wi h he suppo o o he simula ion ools.
Denkena e al. [11] applied a s ochas ic me hod o p edic su ace
opog aphy wi h high accu acy, conside ing p ocess impe ec ions and
kinema ics. Howe e , i equi es p io knowledge o he milling esul s
o a su ace machined unde such p ocessing condi ions, which makes
gene al implemen a ion in so wa e di icul .
Se e al app oaches can be conside ed o he geome ical model o
he cu e . The mos common a e he analy ic model o he helix, he ool
dome, and he in ini esimal cu ing-edge (ICE) elemen . The choice be-
ween hem will depend on he dep h and p ecision equi ed o he
analysis. Lazoglu and Liang [12] modelled he engagemen and he chip
hickness a ia ion du ing con olu ion o p edic he milling o ce o
ball-end milling on a la su ace. Zhang e al. [13] disc e ized he ool
edge o a ball-end ool ip wi h a cons an helix in o a se ies o cu ing
poin s o include he ool wea on he opog aphy su ace p edic ion.
Al hough he e is a conside able amoun o esea ch on ball-end milling
on la su aces, i s p oposed applica ion o milling ee- o m su aces
s ill aces se e al limi a ions due o he complexi ies and changes in he
CWE.
Ismail Lazoglu [14] solid-modelled he CWE o he 5-axis o p edic
he cu ing o ce es ima ion. Howe e , his app oach is compu a ionally
hea y and no p oduc i e. A e xe e al. [15] included ool un-ou by
adding a adial o se o he in ini esimal edge elemen , hus modi ying
he chip hickness. In hese s udies, he models conside ed he uncu
chip hickness, and he e is a limi ed dependence on he ool geome y.
Layegh and Lazoglu [16] analy ically modelled he su ace ob ained in a
5-axis ball end milling conside ing lead angles and ool un-ou , showing
ha he ool o ien a ion a ec s he su ace ex u e. Howe e , he
a e age e o ob ained on a la su ace was abou 20 %. Gou e al. [17]
modeled 5-axis lank milling wi hou disc e iza ion o he cu ing edges.
The model included a iable helix angle combined wi h un-ou o
pe o m he eal ace o 5-axis milling and p ecisely p edic he su ace,
howe e , i is no se led so a o ee- o m milling wi h ball-end
ool ips.
Di e en app oaches can be applied o model he cu e con ac
be ween he ool and he su ace; he mos compu e -e icien me hod is
he analy ical one, which is e y limi ed and used mo e o ideal cu ing
condi ions. Howe e , he ma hema ical model o he su ace is p o ec ed
by he co e o he CAD so wa e, and expo ing his da a is no i ial, so
mos o all s udies ega ding ball-end milling o ee- o m su aces used
mono onic o inclined planes [18].
Disc e e and semi-disc e e models o he su ace a e he mos
commonly used o disc e ize he cu e wo kpiece engagemen (CWE)
du ing ball-end milling. I is know ha he local slope o he su ace
p oduces CWE oscilla ions a ec ing he cu ing speed and oscilla ing he
cu ing o ces, damaging he p ocess [19]. Thus, disc e izing he su ace
in o small and known segmen s o calcula e ins an aneous solu ions
makes i possible o p edic poin - o-poin mo e complex p oblems like
ee- o m milling, up o now e y limi ed [20]. Fu he mo e, some
s udies ha e al eady add essed he CWE calcula ion using pos -
p ocessed NC iles and he CL da a o compu e cu ing su aces
[21,22], bu e o s associa ed wi h he une en poin dis ibu ion a e s ill
a limi a ion, especially o 5-axis machining.
Mos o he s udies o ee- o m su aces a e limi ed o he 3-axis,
whe e he posi ioning o he ool is always in he z-di ec ion, easing
he iden i ica ion o he pai o CL CC and espec i e ec o s. Mo e
complex milling, conside ing 5-axis oolpa h p og amming, equi es
de ailed in o ma ion on he ool o ien a ion as well as he su ace in-
o ma ion. Tunc and Budak [23] de eloped a me hodology o ob aining
simula ion da a in 5-axis milling using CL da a gene a ed by CAM
so wa e. Howe e , hei p oposed me hodology equi es compa ing he
CAM ile wi h one using he same s a egy gene a ed using null il and
lead angles o de e mine CC and i s espec i e ec o as well as an STL o
he su ace, which inc eases p e-wo k and limi s i s applica ion o
gauge- ee su aces.
The ecen g ow h o Indus y 4.0 p omo es machines and so wa e
in eg a ion o p edic o con ol manu ac u ing p ocesses, bu in eg a-
ion wi h CAD/CAM so wa e is s ill a limi a ion [24]. Thus, de eloping
a me hodology based on he CAM so wa e, which conside s he
embedded CAD geome y, o ob ain da a o modelling 5-axis ball-end
milling is s ill necessa y o academic and indus ial pu poses.
These di icul ies lead o he wide use o empi ical me hods in he
shop loo and con ocal mic oscopy imaging analysis, which is ime-
consuming. This echnique uses mic oscopy and lase ligh il e s o
ep oduce he high- esolu ion su ace ex u e, which is alid o in-
spec ion and su ace model alida ion [25]. The accu a e e alua ion o
he opog aphy will e eal ib a ional and mo e complex p oblems
p esen in he manu ac u ing p ocess. On he one hand, mixing all he
damages makes ha d he in es iga ion o indi idual e ec s. On he o he
hand, i allows an accu a e opog aphy p edic ion conside ing eg es-
sion wi h he geome ical model and all he noise ob ained e alua ing
he su ace [1].
Ano he me hod o e alua e he su ace is compa ing local esul s
wi h he heo e ical oughness. Al hough su ace oughness has been
mo e ep esen a i e, lineal oughness is mos commonly used o e al-
ua e he su ace due o he p ice and e sa ili y o he 2D ugosime e
(ISO 1302, highligh ing he 2D pa ame e s Ra, R , Rz). Howe e , i
should be aken in o accoun ha di e se p o iles can display iden ical
oughness pa ame e s and pe o m mechanically di e en ly [26]. Ac-
co ding o Mali and Gup a [27], he su ace oughness o ball-end
milling can be ma hema ically p edic ed wi h high accu acy ega ding
he scallop’s heigh . The scallop heigh measu es he heigh o he
highes poin o he ma k le by he ball-end ool ip and he lowes o
he ollowing cu ing s ep. Howe e , his is only alid when he ma e ial
is shea ed om he su ace.
Scandi io e al. [28] e alua ed he oughness o a ee- o m su ace
a e a milling ope a ion using a ball-end ool ip. The au ho s iden i ied
ha he oughness is in luenced mos ly by he CWE and ool wea bu
did no conside he ool un-ou , which is equi ed o ob ain a mo e
p ecise simula ion. U bikain and Lacalle [29] e alua e he e ec o he
ICE elemen o end mills on he oughness. They obse ed ha he lead
F. Ma in e al.
Enginee ing Science and Technology, an In e na ional Jou nal 55 (2024) 101757
3
and helix angles had less in luence on he a e age oughness o his
kind o ool, while he il angle educ ion imp o es su ace oughness.
Ano he aspec ha is highligh ed in ball-end milling is he e ec o
he ool ip. The ool ip can nega i ely a ec he cu ing p ocess by
inc easing he componen s o he cu ing o ce, inc easing he ool wea ,
modi ying he di ec ion o i s componen s, and o he ela ed p oblems
ha damage he su ace. Fu he mo e, ool ip wea can lead o su ace
in eg i y issues, such as oughness, i egula i y, and damage o he
machined su ace ha acili a es he co osion and a igue p ocess.
Op imized eed a e and cu ing speed cu ing condi ions can minimize
he ool ip e ec bu canno comple ely elimina e i .
The cu ing speed is null a he cen e and nea by egions, esul ing
in a cu ing phenomenon known as plowing. When he minimum chip
hickness is no achie ed, he ma e ial is c ushed ins ead o shea ed.
Thus, ool inclina ion is always p e e able o a oid ool ip cen e con ac
[30]. Howe e , due o geome ical cons ain s, some imes i is impos-
sible o e ade he ool ip o nea by egions, esul ing in a su ace wi h
se e e plas ic de o ma ion, side low, sc a ching, and ca i ies. Also,
se e al pull-ou s and high esidual s esses can be ound wi h di e en
magni udes acco ding o he machined ma e ial [31,32]. These ma ks
le on he su ace a e ha d o p edic bu easy o iden i y in a pos -
e alua ion wi h op ical imaging analysis. Knowing he idealized su -
ace can imp o e he iden i ica ion and a be e comp ehension o he
p ocess. Modeling he inish milling conside ing he ool’s e ec i e
adius is essen ial o include he plas ic de o ma ions and a p ope
su ace p edic ion.
Also, in many s udies, he e ec o he ool o ien a ion is in es i-
ga ed, mi iga ing a ia ions in he opog aphy wi h he ool il and
cu ing di ec ion. Oli ei a e al. [33] quan i ied geome ic e o s on 4-
axis milling o hin-walled pa s in up-cu ing o down-cu ing. The
au ho s a ibu ed he o m de ia ion o he cu ing o ce bu did no
e alua e he su ace oughness and he ool un-ou owa ds ad ancing
he milling p ocess simula ion. Chen and Huang [34] s udied he su ace
opog aphy o ball-end milling conside ing he cu ing-edge geome y.
The au ho s e alua ed he scallops o he su ace o speci ic ool in-
clina ions. Til ing he ool abo e 10◦p opi ia ed a be e su ace
oughness o mos ool diame e s. Liu e al. [35] ecommend inc easing
he lead angles up o 45 deg ees on ball-end milling o achie e be e
oughness alues. The au ho s a ibu e his imp o emen o he
inc eased e ec i e cu ing speed and dec eased eloci y g adien . Be-
sides, he ma ks le on he eed di ec ion we e abou 3 o 4 imes mo e
sensi i e o ool inclina ion han he ones le by he la e al passes o he
su ace oughness.
One way o in es iga e he quali y o he manu ac u ing p ocess is by
di ec ly analyzing he ex u e le on he machined su ace. The milling
p ocess has in e mi en and epe i i e pa e ns ha can cha ac e ize he
su ace and he p ocess. Du ing he cu ing, he o ien a ion o he cu ing
edge changes pe iodically wi h he o a ion o he spindle and eed and,
hus, by he eed pe oo h, making pe iodic ma ks o e ime on he eed
di ec ion. These ma ks a e no well p edic ed in he simplis ic simula-
ion ool o comme cial so wa e (Fig. 1), making he p ocess p edic ion
and su ace e alua ions challenging and uled by empi ical knowledge.
Besides he in e se cinema ic o he 5-axis machining, he complexi y o
he engagemen o he ool wi h he wo kpiece and limi a ions on
expo ing he su ace da a make he p ocess modeling di icul o ee-
o m su aces.
Nowadays, he e a e some models o p edic opog aphies and o he
aspec s o he milling p ocess ha include o ces and hei de i ed
p oblems. Howe e , he e a e many limi a ions when ee- o m su aces
and 5-axis milling a e in ol ed due o se e al da a inpu s equi ed and
bounda y condi ions. Addi ionally, s udies wi h ee- o m su aces
usually use ball-end ool ips ha esul in mo e complex geome ic
p oblems, equi ing su ace da a o modeling ha is usually p o ec ed
by he CAD/CAM so wa e. So, i is common o ind limi ed o idealized
s udies wi h speci ic geome ies, con ac condi ions, o cu ing
pa ame e s.
To ob ain a obus milled model o p edic he ex u e o ee- o m
su aces, including ma e ial p ope ies, he e ec i e cu ing speed o
he ool ip, eed a e oscilla ion, ool un-ou , cu ing pa ame e s, as well
as cu ing geome ies and CWE geome ical model, is necessa y. In his
con ex , he cu en wo k p oposes modeling and in es iga ing he
su ace ex u e le a e ee- o m milling wi h con en ional ball-end
ool ip. Conside ing he c es heigh on he eed di ec ion. The e o e,
a me hodology o compu ing ee- o m su aces is p oposed based on
he disc e iza ion o he oolpa h ob ained by a pos -p ocessed NC ile,
imp o ing he CAD/CAM es ima ion and boos ing indus ial applica-
ions. Fu he mo e, a ou ine is de eloped o ob ain da a o gene al 5-
axis milling o ee- o m su aces, using his da a o su ace p edic ion
Fig. 1. Typical su ace p edic ion by comme cial CAM so wa e.
F. Ma in e al.
Enginee ing Science and Technology, an In e na ional Jou nal 55 (2024) 101757
4
and easy u u e e alua ions o mo e complex p oblems ha equi e
geome ical da a o he ool and he su ace.
2. Ma e ials and me hods
Conside ing he limi a ions o he cu en CAM so wa e o
simula ing he eal ex u e o a machined su ace, p edic ing he cu ing
o ce and he geome ic e o s, among o he s, he p esen wo k p esen s
a new app oach o ob aining in o ma ion di ec ly om he CAD/CAM
so wa e by he CAD geome y and he oolpa h (CC and CL da a) which
can be used o u he de elopmen s. The cu en s udy employs his
me hodology o p edic he machined su ace ex u e o milling ee-
Fig. 2. Flowcha o he p oposed me hodology o su ace p edic ion.
Fig. 3. NX Open ou ine schema ic and lowcha .
F. Ma in e al.
Enginee ing Science and Technology, an In e na ional Jou nal 55 (2024) 101757
5
o m shapes in 5-axis machining.
The me hodology consis s o disc e izing he complex su ace du ing
a 5-axis milling ope a ion and calcula ing he ool and su ace ins an-
aneous posi ions along he oolpa h. This app oach can also be
ex ended o p edic mo e complex p oblems dependen on he o ce,
conside ing bo h CL (Cu e Loca ion) and CC (Con ac Condi ion) da a.
The p oposed de elopmen was o ganized in o six opics. Fi s is
p esen ed a (2.1) o e iew o he p oposed me hodology, hen he (2.2)
ou ine o da a collec ion de eloped in he so wa e Siemens® NX is
desc ibed, ollowed by he (2.3) geome ical modeling o he ool ip,
(2.4) oolpa h da a ea men , and (2.5) su ace p edic ion is p esen ed
wi h wo modeling app oaches. The i s one conside s he ins an a-
neous posi ion o he ool ip o p edic he su ace ex u e. In he second
one, he ajec o y o he in ini esimal elemen s o he ool a e aken in o
accoun o imp o e he la e al oughness p edic ion o he milling p o-
cess. In bo h cases, he e ec o he ool un-ou was conside ed. Finally,
he ma e ials and me hods o e alua ing he implemen ed ou ine and
he ma hema ical modeling a e p esen ed (2.6).
2.1. P oposed me hodology
A p og amming ou ine was de eloped o ob ain a se o da a
necessa y o modeling he su ace. The i s s ep o he p oposed
me hodology is ob aining any complex su ace’s cu ing con ac (CC),
cu ing loca ion (CL), and espec i e no mal ec o s by an implemen ed
ou ine on he CAD/CAM so wa e. A s anda d language C#, was used in
he p og amming ou ine because i is compa ible wi h he open in e -
ace (NX Open) o he so wa e used – Siemens® NX. I is wo h no ing
ha he same me hodology can be adap ed o o he so wa e p og ams
ha ha e an open p og amming in e ace.
Then, a geome ical model was de eloped based on he ou ine
ou pu s o p edic he ball-ended cu ing-edge mo emen and he su -
ace o 5-axis milling. In his second s ep, he geome ies o he ool we e
ma hema ically modeled wi h a scope limi ed o ball-end ool ips wi h a
cons an helix angle. In his s ep, wo app oaches we e conside ed. The
i s conside s he dome a e a comple e o a ion o he ool (ins an a-
neous posi ion), and he second one conside s he ochoidal mo emen
o he ins an aneous cu ing-edge (ICE) elemen (ponde ed mo emen ),
which allows o include, i.e., he ool un-ou . A e ha , bo h da a we e
used o su ace ex u e e alua ion, measu ing opog aphy, scallop
heigh , and heo e ical oughness. Fig. 2 p esen s he lowcha o he
p oposed me hodology.
2.2. Rou ine o da a collec ion
Fo su ace mapping, a ou ine was de eloped using an API (appli-
ca ion p og amming in e ace) on he so wa e Siemens® NX 1953 o
ob ain a lis o he cu ing loca ion (CL), cu ing con ac (CC), and
espec i e ec o s. These da a we e ob ained ollowing a se ies o p o-
cedu es in acco dance wi h he de eloped ou ine.
The i s equi emen is impo ing o modeling he wo kpiece ge-
ome y in he so wa e, ollowed by he usual CAM p og amming. Thus,
bo h geome y and ajec o y will be a ailable o compu a ion and
pos e io milling. As a second equi emen , i ob ains he pos -p ocessed
NC p og am ile in he s anda d o ma (Cu e Loca ion Sou ce File −
CLSF), p o iding no malized da a o he ou ine con aining he CC and
CL da a. In he case o he Siemens® NX so wa e, he CC da a we e
ob ained h ough CAM pos -p ocesso once he ou pu Con ac Da a is
enabled. Then, wi h he pa h and di ec o y o he expo ed CLSF ile o
he da a ex ac ed di ec ly by he so wa e ou ine, a se ies o il e s and
so s a e done while he ou pu da a missing is compu ed line-by-line –
he su ace no mal ec o s o a gi en con ac poin .
An NX command was used o ob ain he ec o no mal o he su ace
on a speci ic CC loca ion. The command inpu equi es a su ace and a
poin o calcula e he no mal di ec ion. Thus, a speci ic CC poin is used
o selec ing bo h he posi ion and he su ace. The su ace selec ion was
au oma ed by selec ing he ea u e objec closes o i s speci ic CC poin .
Finally, he uni a y ec o ela ed o he CC is calcula ed using a suppo
line wi h i s espec i e ex eme poin s, and hen all he ea u es in ol ed
a e des oyed; his p ocedu e is de ailed in Fig. 3.
Highligh ha mos CAD/CAM so wa e has closed a chi ec u e, so
ob aining da a ela i e o he su ace in a speci ic posi ion is no i ial.
A he end o he calcula ion, all he non-cu ing mo es lines a e il e ed,
and he o he lines a e p esen ed in a s anda dized ile wi h 12 columns.
The i s h ee columns ep esen he x, y, and z coo dina es ela ed o
he CL poin s, columns 4, 5, and 6 p esen ec o s i, j and k ( ela ed o
he ool o ien a ion), columns 7, 8, and 9 ep esen he x, y, and z co-
o dina es o he espec i e CC poin s, and he las h ee columns
ep esen he q, , and s, ec o no mal o he su ace on a gi en CC
poin , as exempli ied in Fig. 3.
2.3. Geome ical modeling o he ool ip
Fo he ool modeling, a e e ence sys em was de ined using he
igh -hand ule and he cen e o he ool ip, wi h a clockwise o a ion
on he ool axis, as depic ed in Fig. 4. Then, he ool is ma hema ically
modeled. The local adius is calcula ed acco ding o he ool’s heigh .
Then, he axial and adial imme sion angles a e calcula ed o desc ibe
he edge posi ion inside he ool’s dome. Finally, he e ec o he ool
un-ou in ball-end ool ips can be included as a unc ion o he ool’s
heigh – (z). Fig. 4 p esen s he ball-end ool schema ic.
Conside ing he gi en e e ence sys em a he end o he ool ip, Eq.
(1) gi es he coo dina es o he dome o a ball-end ool ip.
⎧
⎨
⎩
xi=Rsin(ki)sin(θi)
yi=Rsin(ki)cos(θi) o 0◦≤ki≤90◦
zi=R−Rcos(ki)
(1)
Whe e R is he adius o he ool, ki is he axial imme sion angle
adjacen o he e ex C (0, 0, R), shown in ed in Fig. 4. Fo a gi en
angula posi ion θi, ki de ines he posi ion o he poin P along he ool
Fig. 4. Tool schema ics o single adius ool ips.
Sou ce: h ps://www.geogeb a.o g/m/hkd 6 hj
F. Ma in e al.
Enginee ing Science and Technology, an In e na ional Jou nal 55 (2024) 101757
6
helix using Eq. (1).
To model he cu ing edge, in ini esimal elemen s i mus be de ined
as a unc ion o he heigh . Conside ing ha he angula posi ion in-
c eases as he heigh inc eases, a helix can be de ined a he ool dome.
De ining an angula e e ence ∅ measu ed om he X-axis and he
angula inc emen wi h heigh as φi, i gi es he angula posi ion θi, Eq.
(2).
θi=∅−φi(2)
Whe e he angula inc emen wi h heigh φi is de ined by he angen
a a gi en poin wi h a plane pe pendicula o he ool axis, Eq. (3).
an
α
=RΔφ
Δz∴ an
α
i=Riφi
zi
(3)
Conside ing ha he ball-end ool ip has a cons an helix angle, he
in ini esimal edge inc emen wi h heigh can be exp essed by Eq. (4).
φi= (1−coski) an
α
(4)
Combining Eq. (1) o Eq. (4) is possible o de ine he edges o a ball-
end ool ip wi h a cons an helix angle.
Run-ou
ρ
in ol es bo h manu ac u ing e o s and clamping miss
alignmen o he ool-holde sys em. I can be desc ibed as a unc ion o
he local adius wi h he heigh , Eq. (5), hus dependen on he mic o
edge elemen and elian on angula posi ion and axial imme sion
angles.
j(z) = (z) +
ρ
(z)(5)
Whe e j(z)is he local adius o he mic o edge elemen ela ed o
he j lu e, (z)is he local adius o he ool, and
ρ
(z), he adial de i-
a ion o he espec i e mic o edge elemen depends on he elemen ’s
posi ion in he space. Conside ing an ideal manu ac u ing p ocess o he
ools,
ρ
(z)can be app oxima ed o a linea unc ion wi h a e e ence
sys em as an o se (in he xy plane) and il (
τ
) om he e e ence ool
axis, Eq. (6).
ρ
(z) =
ρ
0(x,y) + (z,θ)(6)
Fig. 5 ins an aneously exempli ies he linea mo emen o an in in-
i esimal edge elemen i wi h he e ec o he ool un-ou on he op
iew. Addi ionally, o he ac o s, such as ini ial ool wea and he mal
expansion, can be modeled simila ly as a unc ion o he local adius bu
a e no conside ed in his wo k.
Fig. 5 shows ha in he milling p ocess wi h un-ou , i is possible
ha only one oo h gene a es he su ace, so i is p oposed a simple
calcula ion o adjus he su ace p edic ion based on he eed-pe - oo h,
ool un-ou , and he numbe o ee h. The logic consis s o compa ing
he bigge e ec i e adius ( 1= max), sub ac ing he heo e ical c es
wa e (h
c
) and compa ing i o he o he ee h; i he alue o he e ec i e
adius is smalle , i will no pa icipa e in he su ace gene a ion. Also,
he index numbe o hose ee h mus be sa ed o plo ing. The a e age
dis ance o he su ace eed-pe - oo h ma k is gi en by Eq. (7).
z= z(z
zc)(7)
Whe e zc is he numbe o ee h pa icipa ing in he su ace gene a-
ion, gi en by Eq. (8).
zc=∑
z−1
i=1
1+i:{i=1i z> 1−hc;else i =0}(8)
2.4. Toolpa h da a ea men
Using he ool geome y (sec ion 2.3) and he oolpa h gene a ed by
he CAD/CAM (sec ion 2.2), wi h wo p ocedu es, i is possible o p e-
dic he su ace wi h an e o lowe han he ole ance band used in he
oolpa h gene a ion. The i s is calcula ing he ins an aneous posi ions,
ponde ing he known con ac posi ions (2.4.1). The second one is
compu ing he angula posi ion o he cu ing-edge elemen acco ding o
he ool il and oolpa h da a (2.4.2).
2.4.1. Ins an aneous posi ion e alua ion
Usually, he spindle speed is much highe in he milling p ocess han
in he eed, making he spindle speed e ec on he su ace opog aphy
highe han he eed pe oo h [36]. So, i is possible o conside ha a
comple e o a ion happens ins an ly, emo ing he ma e ial. Howe e ,
in a disc e e model, his assump ion leads o an addi ional e o asso-
cia ed wi h he di e ence be ween he segmen ’s leng hs om he eed-
pe - oo h (
z
). Thus, a good co ela ion be ween hese pa ame e s is
impo an o he model’s accu acy. When he segmen leng h is bigge
han he
z
, mo e ma e ial is emo ed, while when
z
is bigge , he ma-
e ial is unde es ima ed. O he wise, i is necessa y o calcula e in e -
media y poin s o disc e ize he mo emen .
Na u ally, on complex su ace milling, he dis ance be ween he NC
poin s changes depending on he su ace’s ole ance band and local
cu a u e. So, i is necessa y o in e pola e he mapped su ace da a
ob ained by he ou ine acco ding o he
z
used o inc ease modeling
accu acy. Fig. 6 p esen s a schema ic o he me hod applied o compu e
in e media y poin s using he CL and i s espec i e ool o ien a ion.
In he p ocess o disc e izing in e media e posi ions, hei espec i e
uni a y ec o s a e also calcula ed. I is known ha he uni a y ec o o
he ool posi ion (n ) ob ained om he p ocessed 5-axis CL ile can be
w i en in e ms o ijk posi ions gi en he o hogonal ca esian com-
ponen s ela i e o x, y, and z, Eq. (9).
n =nxi+nyj+nzk(9)
The da a ob ained using he ou ine gi es he ins an aneous angen
plane o he su ace, desc ibed by he espec i e poin CC and he uni-
a y ec o ns, Eq. (10).
Fig. 5. Cen e de ia ion caused by un-ou a a gene ic zi plane o he ool.
Fig. 6. Schema ics o oolpa h adjus men o su ace p edic ion conside ing
ins an aneous posi ions.
F. Ma in e al.
Enginee ing Science and Technology, an In e na ional Jou nal 55 (2024) 101757
7
ns=nxq+ny +nzs(10)
To calcula e he ins an aneous di ec ion (
i), he p oduc o he
uni a y ec o s ela i es o CC and CL is compu ed, Eq. (11). And by he
c oss-p oduc o he ool posi ion wi h he local su ace ec o , Eq. (12),
i is ob ained he ins an aneous la e al pass gi.
i=ns×n
|ns×n |(11)
gi=ns×n (12)
2.4.2. Adjus men o he angula posi ion wi h he oolpa h
I he spindle speed is no conside ably highe han he eed o a
be e es ima ion is equi ed, he angula posi ion o he ool edge mus
be conside ed. Addi ionally, cu ing-edge o ien a ion is equi ed o
include he e ec o he ool’s helix and he un-ou on he su ace
es ima ion. Thus, an addi ional p ocedu e was de eloped, adjus ing and
synch onizing he angula posi ion wi h he eed (axial mo emen o he
ool). Equa ion (13) exp esses he angula posi ion in e ms o he
nominal eed pe oo h, which allows he compu a ion o he angula
posi ion o each CL (o in e media y poin s) acco ding o he ool’s
displacemen .
z=ΔdT
i+1− i
=Δd
i+1− i
2
π
ω
(13)
Whe e Δd is he dis ance be ween consecu i e CL poin s, T is one
o a ion pe iod,
ω
he angula eloci y, and i+1 and i a e espec i ely
he in e media e and he ini ial posi ion du ing one o a ion.
Conside ing ha he ool has a cons an angula speed (
ω
), i is
possible o indi ec ly co ela e he eed dis ance co e ed wi h he
angula posi ion (θ). Spli ing he oolpa h in o cons an in e media y
poin s will also esul in a cons an Δθ. Wi h his conside a ion and
knowing he o al dis ance co e ed by he ool, i is also possible o
ob ain he angula posi ion o any mic o edge elemen s on he oolpa h.
Fig. 7 p esen s a 2D schema ic o a Δθ weigh ed in e pola ion be ween
he CL poin s.
Howe e , when new da a poin s a e gene a ed, i is necessa y o
compu e he ela ed ool’s il . I is done by adjus ing o he p e iously
known uni a y ec o s and ponde ing wi h known posi ions. Fu he -
mo e, in bo h me hods p esen ed, ins an aneous o ponde ed mo emen
in e pola ion, he da a c ea ed can be used o any su ace. In he spe-
ci ic case o angula in e pola ion (Δθ), he disc e iza ion p ocess is
mo e c i ical and mus be op imized o ob ain a good co ela ion be-
ween he p ecision and he compu a ional ime. The smalle he Δθ, he
be e he p ecision, bu he highe he compu a ional ime. Thus, he
ochoidal oolpa h o he ICE elemen s can be g aphed using poly-
nomial eg essions (cubic spline) o imp o e p ocessing ime and
main ain accu acy.
2.5. Me hodology o su ace e alua ion
Fi s , he da a we e so ed acco ding o he pa ’s wo ld coo dina e
sys em (WCS) o easy g aphical isualiza ion and e alua ion o he
su ace. To do so, a mesh a he xy plane was c ea ed conside ing he
maximum and minimum posi ions o he NC code, lea ing he high in z
o be compu ed conside ing he ins an aneous posi ions and he
ponde ed mo emen o he ool. Fo each speci ic posi ion, he minimum
(o maximum) z high is compu ed. The ools dome o in ini esimal edge
elemen was ansla ed and o ien ed acco ding o (WCS) using he
p ocedu e desc ibed in Fig. 8. He ea e , each geome ical ea u e was
o ien ed acco ding o he da a ob ained by he ou ine and op imized
wi h he p ocedu e p esen ed in he p e ious sec ion, ob aining he z
heigh o each mesh posi ion.
Then, wo di e en me hods we e applied o inspec he su ace
ex u e. The i s was a simple e alua ion o he scallop heigh o mea-
su e he heo e ical oughness in he eed di ec ion. The second is using
he da a cloud o he su ace o compu e he heo e ical su ace.
2.5.1. Scallop heigh conside ing ins an aneous posi ions o he ool
In o de o ob ain a local es ima ion o he su ace, a simple model o
calcula e he scallop heigh is applied. I can be di ec ly associa ed wi h
he oughness and indi ec ly o measu e he quali y o he milling p o-
cess. The ool’s geome y and cu ing pa ame e s eed-pe - oo h (
z
) can
be used o es ima e he heo e ical oughness o he su ace conside ing
he ins an aneous posi ions (disc e ized oolpa h), Eq. (14). The scallop
heigh (hc) also can be used o calcula e he oughness Rz ough Eq.
(15) [37–39].
hc=R⎛
⎝1−
1−( z
2R)2
√⎞
⎠(14)
Rz=∑5
n=1Rzn
n(15)
To apply hese equa ions h oughou he 5-axis ajec o y, he dis-
c e ized model is used o calcula e he de ia ions in ela ion o he
ins an aneous cu ing plane o each posi ion. Thus, he de ia ions a e
ob ained as a unc ion o he local inclina ion o he su ace and a good
app oxima ion o he ac ual su ace oughness.
Knowing ha he cen e o he ool has a low cu ing speed and he
plowing cu ing phenomena is dominan , wo egions we e e alua ed,
he i s in he cen al oolpa h egion whe e he cen e ac s in he cu
and ano he wi h a highe speci ic cu ing speed, bo h on he eed
di ec ion.
2.5.2. Su ace p edic ion using he mesh da a cloud
T ansla ing he ool posi ion and plo ing he minimum z dis ance o
each posi ion o he equally dis ibu ed da a cloud allows he simula ed
su ace o be ob ained. Then, he da a we e compa ed wi h con ocal
mic oscopy esul s o he cu ed su aces (conca e and con ex egions)
and wi h he o m emo ed by Leica Map 6.2 so wa e. Likewise, he
oolpa h o an in ini esimal cu ing-edge elemen was plo ed acco ding
Fig. 7. Schema ics o oolpa h disc e iza ion wi h a cons an Δθ and il
ponde a ion.
Fig. 8. Geome ical o a ion and ansla ion p ocedu e applied o ool dome
and in ini esimal edge elemen s.
F. Ma in e al.
Enginee ing Science and Technology, an In e na ional Jou nal 55 (2024) 101757
8
o a speci ic heigh , ob aining he ochoidal mo emen o he ICE
elemen . The smalle he Δθ used o compu a ion, he highe he p e-
cision o he ajec o y o he elemen .
2.6. Case s udy expe imen al p ocedu e
A bladed shape pa con aining ee- o m conca e and con ex su -
aces was designed using he so wa e Siemens® NX and manu ac u ed
o e alua e he p oposed me hodology. The ma e ial used was a solid
bulky cylinde wi h a nominal diame e o 46.5 mm o Waspalloy AMS
5706, he nominal composi ion p esen ed in Table 1. The machine used
o manu ac u e he blade was a mul i ask machining cen e Mazak i200
wi h smoo h machining con igu a ion (SMC) by de aul (balanced). The
milling expe imen s we e conduc ed u ilizing he machine’s ails ock.
The blade was inished using a ball-end ool ip wi h a 5 mm adius
manu ac u ed in mic o g ain solid ca bide wi h 10 % Co coa ed wi h
Table 1
Composi ion o Waspalloy- AMS 5706.
Ni C Co Mo Ti Fe Al Z C Mn
58.64 19.34 12.27 3.82 3.04 1.35 1.33 0.05 0.04 0.03
Si Cu B Mg P N S Se Pb Ag
0.03 0.02 0.005 0.005 <0.001
a)
b)
Fig. 9. a) Pa model and machining s a egies. b) P ese ing esul s.
Fig. 10. P og ammed ou ine o 5-axis da a acquisi ion ou pu s.
F. Ma in e al.
Enginee ing Science and Technology, an In e na ional Jou nal 55 (2024) 101757
9
mul ilaye TiSiN (3800 HV 0.05) wi h ou lu es and a 30◦helix angle.
The ool was moun ed on a high- o que ool holde wi h a 40 mm
can ile e , and a p ese e Zolle ® Sma Tcheck 600 was used o measu e
ool leng h and he s a ic un-ou , as depic ed in Fig. 9b.
The milling ajec o ies we e p og ammed on he so wa e Siemens®
NX, conside ing ough, semi- inishing, and inishing ope a ions. A spi al
oolpa h wi h 0.4 mm o a
e
was used in he semi- inishing ope a ion,
lea ing he pa wi h 0.4 mm s ock o he inishing ope a ion. The
inishing p ocess was conduc ed in down-milling wi h cons an a
p
(0.4
mm), a
e
(0.2 mm),
z
(0.05 mm/ oo h), and cu ing speed o 80 m/min
(pa ame e s ecommended by he ool make ). Then, h ee di e en
egions wi h 10 mm leng hs we e e alua ed using, in all o hem, a 5-axis
spi al s a egy (wi h a 0.01 mm ole ance band). This s a egy a oids
ool en ances and exi s ha damage he su ace and comp omise i s
in eg i y. Also, he di ec ac ion o he ool ip was a oided by il ing he
ool in he eed di ec ion. Th ee cu ing engagemen s we e assessed, one
in each egion, 5, 15, and 25 deg ees, espec i ely. Fig. 9a depic s he
oolpa h s a egies.
The p ocedu e p esen ed in sec ion 2.5.2 was applied o inspec he
manu ac u ed pa s. A con ocal mic oscope Leica® DCM3D oge he
wi h he so wa e Leica® Map 6.2, we e used o su ace isualiza ion,
oughness measu emen , and da a cloud expo a ion. The su ace da a
was ea ed using Ma lab® 2021 so wa e o compa e he alues wi h
he simula ion p edic ions using he p oposed model. Du ing he da a
ea men , he su ace was analyzed as scanned and wi hou o m, whe e
a 5 h-o de polynomial eg ession was used o ease he oughness and
model e alua ion.
3. Resul s and discussions
The p oposed me hodology and implemen ed ou ine o ex ac da a
o p edic ing and e alua ing ee- o m su ace manu ac u ed by milling
is p esen ed as ollows: 3.1 Rou ine ou pu s, 3.2. Da a ea men and
model ou pu ; and 3.3 S udy case esul s and modeling e alua ion.
3.1. Rou ine ou pu s
Fig. 10 p esen s an example o a 5-axis oolpa h p og am and he
esul s ob ained using he de eloped me hodology. As can be seen, he
igu e p esen s he empo a y ea u es (lines and poin s) used o suppo
Fig. 11. a) Ball-end ool dome and helix edge; b) 5-axis milling on a ee- o m su ace simula ed by he cam so wa e; c) oolpa h da a ea men o ins an aneous
su ace modeling and applica ion; d) oolpa h da a ea men o ice ochoidal mo emen and applica ion.
F. Ma in e al.
