h ps://doi.o g/10.1007/s00170-021-08166-0
ORIGINAL ARTICLE
5-axis double-flank CNC machining o spi al be el gea s ia
cus om-shaped ools—Pa II: physical alida ions and expe imen s
Gaizka G´
omez Escude o1·Pengbo Bo2·Haizea Gonz´
alez-Ba io3·Amaia Calleja-Ochoa3·Michael Ba oˇ
n4,5 ·
Luis No be o L´
opez de Lacalle1
Recei ed: 20 Ap il 2021 / Accep ed: 30 Sep embe 2021
©The Au ho (s) 2021
Abs ac
Recen ly, a new me hodology o 5-axis lank compu e nume ically con olled (CNC) machining, called double- lank
machining, has been in oduced (see “5-axis double- lank CNC machining o spi al be el gea s ia cus om-shaped milling
ools—Pa I: Modeling and simula ion”). Ce ain geome ies, such as cu ed ee h o spi al be el gea , admi his app oach
whe e he machining ool has angen ial con ac wi h he ma e ial block on wo sides, yielding a mo e e icien a ian o
lank machining. To achie e high machining accu acy, he pa h-planning algo i hm, howe e , does no look only o he pa h
o he ool, bu also o he shape o he ool i sel . The p oposed app oach is alida ed by se ies o physical expe imen s
using an ab asi e cus om-shaped ool speci ically designed o a pa icula ype o a spi al be el gea . The po en ial o
his new me hodology is shown in he semi inishing s age o gea manu ac u ing, whe e i ou pe o ms adi ional ball end
milling by an o de o magni ude in e ms o machining ime, while keeping, o e en imp o ing, he machining e o .
Keywo ds 5-axis CNC machining ·Double- lank machining ·Cus om-shaped ools ·Semi inishing ope a ions ·Tangen ial
mo abili y ·F ee- o m shape manu ac u ing
1 In oduc ion
E icien and highly accu a e manu ac u ing o cu ed
geome ies such as ca ansmissions, gea boxes, o o he
doubly cu ed engine pa s is a se ious challenge in many
indus ies like au omo i e o ae onau ic, o name a ew.
Spi al be el gea s, when compa ed o s aigh - oo hed
be el gea s, a e able o un a highe speed [1]anda e
he e o e indispensable elemen s among gea mechanisms.
To achie e smoo h and silen high-speed ansmission,
manu ac u ing wi h a e y high p ecision is essen ial,
e.g., using di ec ace nanog inding [2]. Mo eo e , high
p ecision inc eases du abili y o he manu ac u ed gea s
ha is ano he main objec i e o mode n, sus ainable
manu ac u ing echnologies [3].
T adi ionally, manu ac u ing o spi al be el gea s
equi es specially de iced machines. The e a e se e al
mains eam app oaches o manu ac u e spi al be el gea s:
Gaizka G´
omez Escude o
[email p o ec ed]
Ex ended au ho in o ma ion a ailable on he las page o he a icle.
gea hobbing wi h pe ime e cu (Gleason) [4], cyclo-
palloidal con inuous gene a ion by spi al hobbing (Klin-
gelnbe g and Oe likon) [5], and con inuous gene a ion by
spi al hobbing wi h conical- ype cu (Klingelnbe g) [1].
Howe e , all hese app oaches a e app op ia e o la ge
manu ac u ing ba ches.
In con as , he p oposed app oach aims a low-cos
manu ac u ing o a single wo kpiece and/o eplacemen o
a b oken pa using 5-axis compu e nume ically con olled
(CNC) machining. The ecen ends in gea manu ac u ing
al eady head his di ec ion [6–8], which is well-sui ed
o small ba ches and an economical al e na i e o he
adi ional app oach using an expensi e hobbing machine.
A he same ime, CNC machining is able o keep high
accu acy ha is essen ial o gea manu ac u ing. Ano he
signi ican ad an age o 5-axis CNC machining comes om
he ac ha i can be combined wi h addi i e manu ac u ing
[9]. This ype o hyb id manu ac u ing enables, o example,
gea epai , ha is some hing highly desi able, bu no
possible wi h he adi ional gea -cu ing me hods.
The pu pose o his s udy is o u he ad ance he ecen
geome ic modeling simula ions on 5-axis CNC machining
wi h cus om-shaped ools [10]. Tha is, he pa h-planning
algo i hm does no only look o op imal machining pa hs,
/ Published online: 25 No embe 2021
The In e na ional Jou nal o Ad anced Manu ac u ing Technology (2022) 119:1647–1658
bu also o he shape o he ool i sel [11–13]. While lank
milling wi h cu ed (ba el) ools is known and possible o
inpu ee- o m su aces [10,14] simul aneous angen ial
con ac on wo sides equi es a speci ic inpu geome y. The
ecen nume ical simula ion esul s showed ha o spi al
be el gea s, a cus om-shaped ool admi s enough eedom
o lank-machine a cu ed alley be ween wo spi al gea
ee h wi h a single sweep, ha ing a bi- angen ial con ac
h oughou he mo ion. This newly in oduced me hodology,
called double- lank, he e o e o e s e en mo e e icien
manu ac u ing han adi ional lank machining. On a
concep ual le el, he ools used in his wo k a e e y simila
o small g inding wheels [15–17], i.e., me al co es coa ed
wi h ab asi e pa icles [18,19]. The e o e, he e ec s o
he ab asi e g ains on he su ace ha e o be aken in o
conside a ion.
In his pape , eal machining expe imen s a e conduc ed
o physically alida e he ecen ly p oposed double-
lank machining me hodology. The esul s show ha his
app oach ou pe o ms classical ball end milling by o de o
magni ude in e ms o machining ime and, o he pa icula
spi al be el gea conside ed in his pape , his app oach
is well-sui ed o he semi- inishing s age. The esul s a e
also i ually compa ed agains (single) lank machining
wi h on-ma ke ba el ools wi h a o able esul s o
he p oposed double- lank machining wi h cus om-shaped
ools.
2 P e ious wo k
Manu ac u ing o spi al be el gea s has been s udied o e
se e al pas decades, see, e.g., [1,4,5,20] and o he ele an
e e ences in [20]. The whole loop: design, p oduc ion,
inspec ion and ins alla ion o spi al- oo hed be el gea s is
a complex p ocess ha equi es a special ea men . The e
a e se e al geome ic cons ain s ha need o be sa is ied
o gua an ee smoo h ansmission be ween he cu ing ool
and he ma e ial block: (i) he lank con ac be ween he
conjuga e gea pai ( he ool and oo h) has o be along a
whole line (cu e), (ii) he line con ac is equally dis ibu ed
in he en i e engagemen a ea, and (iii) he line con ac needs
o p ese ed a e e y ins an o he mo ion [4].
T adi ional pipeline o manu ac u ing o gea s is aimed
o la ge ba ches and g oo e-making machines ha ely
on slo ing on cu ed ool. The wo main app oaches:
he con inuous indexing me hod, e e ed o as “ ace
hobbing”, and he single indexing me hod e e ed o as
“ ace milling” p esen some di e ences. The ace hobbing
me hod p oduces an epicycloidal shape in oo h leng hwise
di ec ion. The ace milling me hod is p ocessed in such a
way ha bo h lanks a e manu ac u ed in a single cu , i.e.,
a cons an slo wid h esul s in he oo h oo due o he
ci cula cu e head [21]. While palloid gea s a e p oduced
by a conical hob, he cyclo-palloid gea s a e manu ac u ed
using a ace hob cu e .
This pape belongs o a amily o mode n app oaches ha
ocus on gea s manu ac u ing using uni e sal mul i asking
machines o i e-axis milling cen e s [22,23]. The main
ad an age o his new end s ems in i s e sa ili y as he
ool in gene al does no depend on he gea geome y.
This ac makes he echnology e y lexible as i can be
pe o med on a ious milling cen e s, and no , in con as o
he adi ional me hods (Gleason and Klingelnbe g), on one
speci ic la ge-scale machine.
Suh e al. [8] use a 3-axis milling machine wi h
a o a y able; howe e , ball end milling is applied in
semi- inishing and inishing s ages. A nume ical app oach
o de e mina ion o machine- ool se ings o oughing
o a pinion by using a sp ead-blade ace milling cu e
is p oposed in [3]. Fi e-cu me hod is applied and he
manu ac u ing ime is minimized by maximizing he
ma e ial cu du ing he ough-cu ing s age. T adi ionally,
s anda d ools a e equen ly used o gea s machining
in uni e sal machining cen e s [7]. Howe e , his pape
ollows he ecen end whe e ee- o m ools a e used o
nea - o-ne -shape machining, especially o complex slo s,
such as he oo h space o he gea .
Fo ce ain ype o gea s, such as non-ci cula spu
be el gea , he i egula shape makes he design and
manu ac u ing p ocess e en mo e di icul and o ging s age
is in ol ed o dis ibu e he ma e ial acco ding o he shape
ea u es o he gea [24]. Ano he issue ha needs o
be ca e ully conside ed is su ace oughness. A model o
p edic and con ol he ee h su ace oughness o 3+2 axis
milling using ball end milling has been p oposed ecen ly
[25].
O he ecen wo ks ha e ocused on gea s machining
wi h uni e sal machines using milling echnology [26,
27]. Howe e , inno a i e p ocesses wi h highe ma e ial
emo al a es a e one o he main objec i es in mode n
manu ac u ing. In his line, Supe Ab asi e Machining
(SAM) [28] is one e sa ile and easible solu ion ha
inc eases gea s’ machining e iciency. Speci ically, SAM
p o ides g inding echnology p ecision [29] wi h simila
machining eeds and cos s, bu wi h sho e machining
imes.
This esea ch goes in he di ec ion o e icien spi al
be el manu ac u ing using uni e sal mul i asking machines
o i e-axis milling cen e s, whe e he main objec-
i e is o u he educe machining ime. To his end,
he p oposed esea ch aims a he semi- inishing s age
using highly e icien double- lank machining whe e no
only he pa h o he ool, bu also he shape o he
ool i sel a e he unknowns in an op imiza ion-based
amewo k.
1648 In J Ad Manu Technol (2022) 119:1647–1658
The es o he pape is o ganized as ollows. Sec ion 3
gi es a b ie summa y o he ma hema ical de i a ion o
he cus om-shaped ool design and i s 3D mo ion. Sec ion 4
desc ibes he case s udy and Sec ion 5shows he esul s
ob ained. Finally, Sec ion 6discusses he u u e esea ch
di ec ions and concludes he pape .
3 Double-flank machining
and cus om-shaped ool design
The basic building blocks o he double- lank machining
algo i hm will be b ie ly ecalled, mo e de ails can be ound
in [11]. The p oposed app oach i s ini ializes he mo ion
o he ool using a bisec o su ace o he oo h space and
es ima es he ini ial shape o he ool (Sec ion 3.1), ollowed
by global ool and mo ion op imiza ion (Sec ion 3.2).
3.1 Ini ializa ion o double-flank machining
The goal is o app oxima e he space be ween wo ee h o
a gea , ecall Fig. 1,byanen elope o a gene al ool 
such ha he e is a bi- angen ial con ac be ween and 
on bo h sides o he oo h space (double- lank machining).
The unknowns in an op imiza ion-based algo i hm a e bo h
he machining ool and a uled su ace R( he mo ion
o he ool’s axis). The uled su ace is ep esen ed as a
(3×1)- enso p oduc B-spline pa ch
R( ,s) =(1−s)p( ) +sq( ), [ ,s]∈[0,1]×[0,1],(1)
whe e sis he pa ame e in he di ec ion o ulings and
is he ime pa ame e o he wo bounda y cubic B-spline
cu es p( ) and q( ), o mo e de ails see [11].
Gi en he alley be ween wo ee h o a gea , i s
he bo om pa o he alley is immed o (as his
pa canno be lank-machined anyway). This imming
ope a ion de ines wo side su aces 1and 2.As he
machining ool is aimed o ha e angen ial con ac wi h
bo h 1and 2, he bisec o su ace Bis compu ed.
The bisec o , howe e , is a gene al su ace, and he e o e
(a) (b) (c)
Fig. 1 (a) Spi al be el gea (5-axis CNC machined using he p oposed
me hodology). (b) A zoom-in o one oo h space (aka “ alley”)
be ween wo ee h and i s CAD model ha is o med by a doubly
cu ed ee- o m su ace (c)
spline i ing me hod is used o compu e i s uled su ace
app oxima ion, see Fig. 2(b).
The ini ial uled su ace de ines he ini ial shape o
he machining ool and i s en elopes de ine he ini ial
app oxima ion o he wo su aces 1and 2.The wo
( igh and le ) en elopes 1and 2a e equi ed o
app oxima e 1and 2, espec i ely, as close as possible,
(a) (b)
(c) (d)
Fig. 2 Design o he cus om-shaped ool. (a) A ca i y bew een wo
ee h ep esen ed as a spline su ace. (b) The sel -bisec o B(blue)
is i ed by a uled su ace Rini ( ed) and an ini ial shape, ini,o
he ool is compu ed. The ini ial ool and i s ini ial posi ion may
pene a e he e e ence su ace ( amed in ed). (c) The ool and i s
ajec o y Rbo h unde go global op imiza ion o minimize he e o
o he le (1) and igh (2) en elopes om . The en elopes a e
colo -coded by he dis ance e o dis (i−i),i=1,2, ha mee s
ine machining ole ance o 50 μm. (d) The inal double- lank mo ion
o he cus om-shaped ool  h ough he gea alley
1649In J Ad Manu Technol (2022) 119:1647–1658
and wi hin he gi en machining accu acy ε=50 μm, see
Fig. 2(c).
To compu e he bes en elopes 1and 2,i is
o mula ed as an op imiza ion p oblem. The unknowns a e
he wo cu es p( ) and q( ) (bounda ies o he ule su ace
R) and a scala unc ion d(s) ha de e mines he sphe e
adius in he uling di ec ion s. To compu e he sel -bisec o
Bo , he mo ion o he ool is concep ualized as a wo
pa ame e amily o sphe es (one in ime, second in he
uling di ec ion) ha should ideally ouch on wo sides,
see Fig. 2(b). Bis hen a locus o all such cen e s o
sphe es. The igh and le sides (de ined by imming o
he bo om pa o he alley) su aces 1and 2a e used,
see Fig. 2(b), o compu e B,and hen
F(z)=dis (z,
1)−dis (z,
2), (2)
whe e z∈R3is he desi ed cen e o he sphe e and dis is he
poin -su ace minimal dis ance. The iso-su ace F(z)=0
ha de ines he bisec o Bis compu ed using a a ian o
he ma ching cubes algo i hm, see [11] o mo e de ails.
3.2 Tool and mo ion op imiza ion
In he p oposed op imiza ion-based amewo k, bo h he
ool and i s mo ion, ep esen ed by a uled su ace R,a e
op imized. The op imiza ion has wo main objec i es: (i) o
app oxima e he su ace wi hin a ine machining e o , i.e.,
emo e as much ma e ial as possible and (ii) o gua an ee
ha he en elope o he ool lies inside he alley , i.e.,
he e is no o e cu .
As discussed in Sec ion 3.1, an ini ial uled su ace Rini
is compu ed om he sel -bisec o B. This gi es also, o
each alue o s,s∈[0,1], a se o scala alues ha
co espond o he dis ance dis (R( , s), ) andbya e aging
hese alues o a ious one ob ains an ini ial adial
unc ion d(s). This gi es an ini ial pai o en elopes ini
1
and ini
2. Howe e , hese en elopes, in gene al, in e sec 
which co esponds o o e cu ing, see Fig. 2(b).
To elimina e his phenomenon, he ool ini and i s
mo ion Rini bo h unde go global op imiza ion. The goal is
o op imize hem such ha ini
1and ini
2become as close
as possible o ( emo e as much ma e ial as possible)
and hey bo h lie inside he alley (no o e cu ). To achie e
his goal, we p oceed as ollows. The uled su ace Ris
uni o mly sampled bo h in and spa ame ic di ec ions o
ob ain ij := R( i,s
j),i=1,...,m,j=1,...,n. In ou
disc e e app oach, o each s-pa ame e alue ( ixed j), one
ob ains a se o disc e e alues dij which a e he dis ances
om  o a ixed poin o he axis as i mo es in ime.
Toob ainamo iono  ha is pene a ion- ee wi h (no
o e cu ), we de ine
dj=min
i=1,...,m dij ,(3)
whe e dja e he pene a ion- ee adii. In his disc e e
se up, he pene a ion- ee adius depends on he sampling
densi y. m=100 was se in all he expe imen s; his alue
u ned ou o be su icien ly la ge o e u n s able alues o
he alley shown in Fig. 1.
These adii a e he lowe bounds o he poin -su ace
dis ance o each j, i.e., dis ances ha de ine (disc e e)
adial unc ion ha co esponds o a pene a ion- ee ool,
see Fig. 2(d). Consequen ly, he pene a ion- ee e o is
de ined as
εj=d
j−dj(4)
whe e d
ja e he samples o he ini ial adial unc ion
d. Deno e by da ec o o unknown dis ances d:=
(d1,...,d
n)and op imize bo h, he uled su ace Rand d.
Finally, he objec i e ha a e e y ime ins an he
ool is equi ed o be as close as possible o ,bu also
pene a ion- ee, is o mula ed. This leads o a minimiza ion
p oblem
Fp ox(p,q,d)=1
mn
n

j=1
m

i=1
dis ( ij ,)−dj−εj2→min (5)
subjec o he axis- igidi y cons ain s
F igid(p,q)=p( i)−q( i), p( i)−q( i)−L2=0,(6)
whe e dis (, ) is a poin -su ace dis ance and Lis he leng h
o l. The unknowns in he minimiza ion a e he con ol
poin s o he wo B-spline cu es p( ) and q( ),and he
ec o o sphe e adii d.m=100 and n=30 was se
in he nume ical simula ions. Mo e de ails on he whole
ool-op imiza ion p ocedu e can be ound in [11].
4Cases udy
The esul s o he pa h-planning algo i hm desc ibed in [11]
we e con e ed in o a CL- ile, and consequen ly con e ed
in o a G-code, and es ed in a con en ional machining
cen e , Kondia HS1000, see Fig. 3. The semi inishing
ope a ions we e ca ied ou wi h bo h a ball end ool
and a cus om-shaped ool. The cus om-shaped ool was
capable o bi- angen ial machining, which esul ed in a
simul aneous semi inishing o bo h walls o he oo h space.
One o he objec i es was o educe machining imes in he
semi inishing s age as he cus om-shaped ool admi s wide
s ips o high accu acy and he e o e only a single pa h is
needed, in con as o ball end milling which equi es many
milling pa hs.
Spi al be el gea was selec ed as a case s udy as i is
one o he mos widesp ead componen s in he indus ial
sec o . I is also he elemen pa excellence used o ans e
powe om one elemen o ano he , by ansmi ing ci cula
1650 In J Ad Manu Technol (2022) 119:1647–1658
Fig. 3 5-axis milling cen e
mo ion in e ms o he gea wheel con ac . One o he
mos impo an applica ions o gea s is he ansmission o
mo emen om he sha o a powe sou ce, such as an
in e nal combus ion engine o an elec ic mo o , o ano he ,
end-e ec o , sha . In ei he case, a high accu acy is highly
demanded as he machining e o s in luence signi ican ly
he pe o mance.
The gea wheels can be manu ac u ed om a wide a ie y
o ma e ials o ob ain he igh mechanical p ope ies.
F om he poin o iew o mechanical design, s eng h
and du abili y, i.e., wea esis ance, a e he mos impo an
a ibu es. In gene al, he gea designe should conside he
abili y o manu ac u e he gea , om he o ma ion o he
gea ee h up o he inal assembly o he gea in a machine.
O he conside a ions include weigh , co osion esis ance,
noise, and cos . F-1550 s eel (18C Mo4) was selec ed as
he es ing ma e ial o manu ac u ing o he spi al be el
gea , since i eaches a ai ly good ag eemen wi h all he
cha ac e is ics ha s eel needs o possess. Mechanical and
physical p ope ies and chemical composi ion o he used
ma e ials a e shown in Table 1.
This pa icula spi al be el gea was chosen, because
i s con ac su ace is la ge compa ed o hose o s aigh -
oo hed be el gea s, and his ac poses a g ea challenge
when compu ing bo h he ool geome y and he machining
pa h. The speci ic cha ac e is ics o he wheel and he
heo e ical ma ing pinion o a 5/3 gea a io a e shown in
Table 2.
The es s we e ca ied ou on a con en ional machining
cen e , Kondia HS1000. This machine is a 5-axis milling
machine, wi h 3 linea and 2 a e o a y axes. The linea axes
a e 2 in he head (X, Z) and one in he able (Y), while bo h
o a y axes a e in he indexing able (A, C). The spindle
speed capaci y is 24,000 pm.
Ini ially a 210-mm-diame e and 120-mm- hick s eel
bille was used as a s a ing poin . A se ies o p e ious
ope a ions we e ca ied ou o achie e a geome y close o
he inal. These ope a ions a e shown in Fig. 4 oge he
wi h machining imes needed o each pa icula machining
s age.
4.1 Cus om-shaped ool o SAM
Rega ding he SAM ool, a cus om-shaped ool was used
o pe o m he semi inishing ope a ion o he oo h space.
I s coa was a monolaye elec opla ed CBN g inding wi h
a g ain size o 300 μm, see Fig. 5. A ool o his ype was
chosen due o i s excellen ool wea cha ac e is ics, because
he ab asi e g ains a e esha pened as hey b eak up du ing
he machining p ocess and also because he SAM p ocess
is well adap ed o he calcula ion and manu ac u ing o a
cus om-shaped ool. When manu ac u ing he ool co e, he
hickness o he binding ma e ial and he ab asi e g ains
we e aken in o accoun in o de o ob ain a ool wi h he
exac geome y calcula ed in he modeling s age. The adius
o he ool a ies om 4.8 o 13.2 mm, see Fig. 6,and he
Table 1 Top: F-1550 s eel (18C Mo4) chemical composi ion (%). Bo om: Mechanical and physical p ope ies. The da a a e cou esy o [30]
CSiMnP
max Smax C Mo Cumax
0.15–0.21 0.15–0.40 0.60–0.90 0.025 0.035 0.90–1.20 0.15–0.25 0.40
Ha dness Yield poin Tensile S eng h Densi y
34 HRC 0.88 GPa 1.08 GPa 7850 kg/m3
1651In J Ad Manu Technol (2022) 119:1647–1658

Table 2 Spi al be el gea dimensions
hickness o he ab asi e coa is 0.5 mm. No e ha he ool
has nega i e Gaussian cu a u e (i.e., i is no a conical ool),
see [11] o mo e de ailed analysis on he ool design.
Conce ning cu ing condi ions, hese we e adap ed
owa ds he SAM echnology in his so o machining
cen e s, in pa icula hey we e adjus ed o he spindle
capaci ies, wi h a spindle speed o 24,000 pm, he limi
o he machine, and a eed a e o 250 mm/min. I is
impo an o no e he e ec o cu ing speed on machining,
especially in he con ex o supe ab asi e machining. The
op imal SAM condi ions o he speed o o a ion should
be a ound 60,000–90,000 e olu ions [31]. Howe e , o
achie e hese speeds, high pe o mance heads a e equi ed
which con en ional machines do no ha e.
5 Resul s and alida ion
To physically alida e he esul s o he modeling algo i hm,
he machining pa h o he cus om-shaped ool in he
manu ac u ing o a spi al be el gea was applied. Mo e
speci ically, he cus om-shaped ool was used in he
semi inishing ope a ion, which is he place whe e Supe
Ab asi e Machining echnology has i s po en ial niche o
wo k. In Fig. 7, he alley be ween spi al be el gea ee h
is shown du ing oughing and semi inishing ope a ions wi h
milling and SAM ope a ions. Obse e a clea ly isible
di e ence in he quali y o su ace smoo hness in Fig. 7(a)
and (c).
A quali a i e compa ison be ween double- lank machin-
ing using a cus om-shaped ool and ball end milling, du ing
he semi inishing s age, is p esen ed. Mo eo e , a i -
ual compa ison agains single- lank milling using a ba el
ool is also made. In pa icula , i is shown ha su ace
oughness and manu ac u ing ime a e signi ican ly educed
when using double- lank machining wi h cus om-shaped
ool.
5.1 Su ace oughness
Su ace oughness is one o he key pa ame e s ha
in luence a smoo h mo emen be ween gea s, hei ace-
ace con ac , and consequen ly he li e o he whole
gea . Typically, he su ace oughness is measu ed using
a con ocal mic oscope, howe e , due o he di icul
Fig. 4 P og ess and machining
ime summa y o he whole gea
manu ac u ing p ocess. The
machining ime is o ma ed as
hou s:minu es:seconds
1652 In J Ad Manu Technol (2022) 119:1647–1658
Fig. 5 G ain dis ibu ion and
p o ile
accessibili y o he aces o he gea , esin was applied in
o de o measu e a nega i e o he oo h space.
The p ocess o ob aining he nega i e o he ace
p oceeds as ollows: i s , he a ea o be measu ed is
deg eased wi h he DN1 deg ease cleane p o ided by
PLASTIFORM’s own company (PLASTIFORM, Mad id,
Spain). Once his is done, a closed a ea mus be o med such
ha he luid (liquid esin) co e s bo h sides o he ca i y,
and hen he luid is applied o he measu ing a ea using a
dispensing gun. Finally, cca 6 min is needed o he solu ion
o d y ou , and hen one can emo e he nega i e o he
ca i y, see Fig. 8.
I was selec ed a luid ype esin, so ha i could
low h ough he en i e gea ca i y and hus adap well
o he su ace o he aces. Speci ically, he F65 p oduc
was used, which allows a semi- lexible geome y o
be ob ained, sui able o measu emen by bo h con ac
measu ing sys ems and op ical measu emen sys ems. The
p ecision ob ained wi h his esin is ±1μm.
A Leica DCM 3D con ocal mic oscope was used o
analyze he su ace oughness o he esin. Bo h sides o he
ca i y we e analyzed, as he amoun o excess o ma e ial
was sligh ly di e en on each side a e oughing. The
adjus men o he oughness measu emen in his case was a
cu ing leng h o 0.8 mm and an e alua ion leng h o 4 mm,
acco ding o ISO 4288 [32]. Figu e 9shows he opog aphy
and ela ed da a o bo h sides o he ca i y.
Topog aphy on bo h sides o he oo h ca i y shows
a pe ec ly ecognizable g inding pa e n, in which he e
a e ema ked peaks and alleys along he scanned su ace
caused by he andom dis ibu ion o he ab asi e g ains. I
is no iceable ha sligh ly be e esul s in e m o oughness
we e ob ained on he igh ace, as he oughing ope a ion
lea es ha ace smoo he and s epless be ween passes, jus
he opposi e o he le ace, as i can be seen in Fig. 7(d).
Howe e , his ac is no a limi a ion o he p oposed double-
lank app oach, bu i is due o he ac ha he oughing
s age le he igh ace smoo he .
The esul s a e in acco dance wi h “indica i e su ace
oughness compa ison” ha many companies handle [33].
The oughness alues ob ained we e accep able o a
semi inishing ope a ion because hey a e close o hose
ob ained wi h simila s a egies conside ing hem as
inishing ope a ions.
5.2 Machining ime
Ano he aspec ha was conside ed in his wo k was he
analysis o machining ime du ing semi inishing ope a ions
on gea ee h. To his end, machining ime o ball end
milling ope a ion and double- lank SAM s a egy wi h a
cus om-shaped ool was measu ed, and ba el lank milling
i ual machining ime was calcula ed. The con en ional
semi inishing ope a ion using a ball end mill wi h 4 mm
diame e was used wi h a s epo e o 0.33 mm o dep h
o cu in 3 la e al s eps in each ace and a eed o 2800
mm/min. On he le ace, 20 axial passes we e epea ed
3 imes axially (60 passes o al) while on he igh ace
20 passes we e su icien . In con as , semi inishing using
a cus om-shaped ool was accomplished in a single sweep
wi h he ollowing pa ame e s: a eed o 500 mm/min and
a spindle speed o 16000 pm. In he case o single- lank
milling using a ba el-shaped ool wi h 12 mm o ba el
diame e , in o al 20 passes we e done o co e he whole
su ace wi h a eed o 848 mm/min.
Wi h he abo e-men ioned alues o cu ing pa ame e s
o he h ee manu ac u ing semi inishing ope a ions,
he ollowing machining ime esul s we e ob ained: (i)
con en ional ball end milling: 2 min and 7 s, (ii) double-
lank SAM semi inishing wi h he cus om-shaped ool: 24 s,
Fig. 6 Cus om-shaped g inding
ool and i s geome y
1653In J Ad Manu Technol (2022) 119:1647–1658
Fig. 7 Spi al be el gea
semi inishing ope a ion.
(a) Manu ac u ing wi h SAM.
(b) Vi ual e i ica ion wi h
SAM. (c) Manu ac u ing wi h
ball end mill. (d) Vi ual
e i ica ion wi h ball end mill
and (iii) ba el lank milling: 1 min and 8 s. Double-
lank SAM domina ed in e ms o machining ime. When
compa ing wi h he o he wo, in he case o ball end milling,
he semi inishing machining ime was educed by 81.1%,
sa ing in o al 43 min pe gea . In he case o ba el lank
milling, SAM double- lank machining was 2.83 imes as e
han ba el lank milling. See Fig. 4 o he summa y o he
machining imes o each pa icula s age.
5.3 Dimensional de ia ion
Dimensional de ia ion o he h ee es ed semi- inishing
s a egies: ball end mill ope a ion, double- lank SAM
wi h a cus om-shaped ool, and ba el lank milling we e
quali a i ely compa ed. Figu e 10 shows simula ion esul s
o he h ee semi inishing ope a ions using a comme cial
so wa e.
In he case o he oo su ace o he oo h, he esul s
ob ained by all me hods we e e y simila , eaching a oo h
su ace excess o ma e ial o up o 0.8 mm. The esul s
ob ained on he oo h ace su ace show clea di e ences.
In he case o ball inishing ope a ion, a uni o m inish
was ob ained along he en i e su ace wi h a s ock a ound
0.23 mm. In he case o he SAM, he e a e wo clea ly
di e en ia ed zones. In he i s zone, he igh ace, he
alues ob ained in he semi- inishing a e p ac ically close o
he inal geome y o he piece. On he le side, an unde cu
o 0.1 mm was ob ained along he oo h ace. Compa ing he
abo e-men ioned esul s wi h ba el lank milling, i can be
seen ha he p oblem on he oo su ace is almos sol ed,
excep o he ille adius, whe e is a s ock o mo e han
0.3 mm. Howe e , in he es o he su ace he e is an
Fig. 8 Cu ing p ocess o he esin and i s zoomed-in pa a e
ha dening
1654 In J Ad Manu Technol (2022) 119:1647–1658
Fig. 9 Su ace a ea and p o ile oughness pa ame e s alues o he le ( op) and igh (bo om) side o he gea oo h ca i y
undula ion p o ile ha goes om 0.03 mm in he bo om o
0.21 mm in he peak.
5.4 Discussion and limi a ions
The p oposed app oach signi ican ly educes he semi in-
ishing ime by using a p ope ly designed cus om-shaped
ool. The ool has o be manu ac u ed in ad ance, how-
e e , he cus om-shaped ool cos s a e low, in pa icula :
cylind ical s eel ba F115 (85e) o c ea e 4 SAM ools,
i.e., 21.25epe he s eel co e o he ool, and 45e o add
he ab asi e g ains. In o al, he cos o he cus om-shaped
ool is 66.25e. In con as , he on-ma ke ool o ball end
milling, VF4SVBR0200, cos s 120e.
The su ace oughness alues ange Sa = 2.59–3.87 mm
using he SAM app oach which is a sligh ly mo e han he
numbe s ha can be ob ained by means o con en ional
milling [33]. Ne e heless, hese alues a e accep able in
he case o a wo kpiece which la e unde goes inishing
ope a ions.
Ano he sligh limi a ion is ha he e y bo om o
he ca i y is no accessible wi h he ool whose shape is
designed o double- lank he wo aces o he ca i y. The
bo om o he ca i y has o be machined using ball end
milling app oach.
Compa ing SAM double- lank machining wi h lank
milling wi h ba el ools, bo h app oaches o e simila
accu acy, bu double- lank machining is as e ( ac o o
2.83) due o he ac ha only a single sweep o he ool is
needed.
The p esen ed esul s a e p omising, howe e , he
double- lank me hodology has been es ed on one speci ic
ype o a spi al be el gea , wi h pa ame e s shown in
Table 2. Fo gea s wi h la (plana ) ee h, he double- lank
app oach is no challenging as he ideal mo ion boils down
o a plane-plane bisec o compu a ion. The o he ex eme
o small and e en mo e cu ed e e ence geome y such as,
e.g., pinions has no been expe imen ed wi h, bu can be a
p omising enue o u u e esea ch.
6 Conclusion and u u e wo k
We ha e p esen ed a new a ian o 5-axis lank machining,
called double- lank. In his machining me hodology, no
only he machining pa h, bu also he shape o he ool i sel
1655In J Ad Manu Technol (2022) 119:1647–1658