Ci a ion: Robles, A.; As a loa, A.;
Llanos, I.; Mancisido , I.; Fe nandes,
M.H.; Munoa, J. Compa ison o
Modula ion-Assis ed Machining
S a egies o Achie ing Chip
B eakage When Tu ning 17-4 PH
S ainless S eel. J. Manu . Ma e .
P ocess. 2024,8, 167. h ps://
doi.o g/10.3390/jmmp8040167
Academic Edi o : Shu ing Lei
Recei ed: 27 June 2024
Re ised: 24 July 2024
Accep ed: 25 July 2024
Published: 2 Augus 2024
Copy igh : © 2024 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
Manu ac u ing and
Ma e ials P ocessing
Jou nal o
A icle
Compa ison o Modula ion-Assis ed Machining S a egies o
Achie ing Chip B eakage When Tu ning 17-4 PH S ainless S eel
Ainhoa Robles 1,*, Asie As a loa 1, Iñigo Llanos 1, Ike Mancisido 1, Ma ia Helena Fe nandes 2
and Jokin Munoa 1,2
1Ideko Resea ch Cen e, A iaga Indus ialdea 2, E-20870 Elgoiba , Spain; [email p o ec ed] (A.A.);
[email p o ec ed] (I.L.); [email p o ec ed] (I.M.)
2Depa men o Mechanical Enginee ing, Bilbao Facul y o Enginee ing, Uni e si y o he Basque
Coun y (UPV/EHU), Alameda de U quijo s/n, E-48013 Bilbao, Spain
*Co espondence: a [email p o ec ed]; Tel.: +34-943748000
Abs ac : Chip mo phology is an in insic cha ac e is ic o he machining p ocess ha de e mines
he quali y o he p ocess. When machining low machinabili y ma e ials, he chips o med a e
usually long, con inuous, and di icul o b eak. Due o he nega i e e ec o he accumula ion o
he chip along he p ocess, chip b eakage and he co ec ex ac ion ou o he machining a ea ha e
become indispensable equi emen s. Al hough nume ous chip-b eaking me hodologies ha e been
p oposed, modula ion-assis ed machining (MAM) is one o he mos p omising app oaches, due o
i s independence om he wo kpiece ma e ial, ool geome y, and cu ing condi ions. In his wo k,
a compa ison o di e en modula ion-assis ed machining s a egies, based on he modula ion o
he eed (F-MAM) o he dep h o cu (D-MAM), we e expe imen ally e alua ed and compa ed o
con en ional u ning in e ms o chip mo phology, su ace oughness, and ool wea . Resul s showed
ha bo h MAM s a egies enabled chip b eakage and imp o ed chip e acua ion in compa ison o
con en ional u ning; howe e , D-MAM showed a be e pe o mance in e ms o ool wea and
su ace oughness.
Keywo ds: u ning; modula ion-assis ed machining; chip b eakage
1. In oduc ion
In con inuous machining p ocesses, especially in u ning ope a ions, he e a e many
ac o s ha ha e an in luence on he e iciency o he p ocess and p oduc quali y. In
addi ion, ac o s such as cu ing pa ame e s, ool wea , o chip mo phology need o be
con olled along he machining p ocess o mee he es ablished ole ances and o op imize
p oduc ion ime. Ne e heless, one o he majo challenges in he con inuous machining
p ocess is chip o ma ion. Unlike milling, whe e he ool cons an ly engages and disengages
he wo kpiece, con en ional u ning, bo ing, and h eading ope a ions ypically exhibi
con inuous cu ing, c ea ing long and con inuous chips. This chip o ma ion is usual when
machining aus eni ic low machinabili y ma e ials commonly used by he ae onau ical
indus y, such as nickel-based supe alloys o p ecipi a ion-ha dened aus eni ic s ainless
s eels. This issue is ela ed o he ma e ial p ope ies, as he high ha dness o he ma e ial
demands low cu ing speeds o a oid high ool wea a es, and he aus eni ic na u e o he
me allic ma ix makes i di icul o ake he ma e ial o he b eaking poin and gene a e
discon inuous chips, e en wi h he use o ad anced chip-b eake geome ies. The excess
chip leng h leads o he en anglemen o he chip wi h he ool o wi h he wo kpiece,
making chip e acua ion a g ea challenge. Especially du ing he e ical u ning o big
pa s, he need o emo e he chips om he machine can gene a e he highes p ocess
ine iciencies in a machining ins alla ion. Also, he chip en anglemen can gene a e damages
on he ools and pa s, which can lead o e en g ea e ime losses and, in he case o high
added alue pa s, signi ican ly highe cos s [1].
J. Manu . Ma e . P ocess. 2024,8, 167. h ps://doi.o g/10.3390/jmmp8040167 h ps://www.mdpi.com/jou nal/jmmp
J. Manu . Ma e . P ocess. 2024,8, 167 2 o 14
Howe e , he e a e some echniques ha enable chip discon inui y and, he e o e,
imp o ed chip e acua ion:
•Cu ing ool inse s wi h he chip b eake included in hei geome y.
•Sys ems capable o b eaking he con inuous chip a e i is gene a ed [2,3].
•High-p essu e cu ing luid o de o m he chip and help in i s b eakage [4,5].
•Modula ion-assis ed machining (MAM).
In he p esen wo k, modula ion-assis ed machining is p oposed as a chip con ol
echnique. This is based on nulli ying he unde o med chip hickness in he cu ing p ocess,
adding a ha monic oscilla ion on op o he s anda d mo emen o he ool. Such ha monic
oscilla ion can be added bo h in he eed (F-MAM) o he dep h o cu di ec ions (D-MAM).
This way, he inse pe iodically disengages he wo kpiece, p oducing discon inuous chips.
Conce ning he de elopmen o his echnique, he pionee ing wo ks in his chip-
b eaking app oach we e ini ia ed by Sa el e al. in 1961 [
6
], who desc ibed he kinema ic
condi ions o sinusoidal ool oscilla ions in he di ec ion o he eed (F-MAM). Os wald [
7
]
ma hema ically de ined he equi ed ampli ude o he b eakage o he chips, showing ha
he minimum ampli ude o b eak he chip is ob ained o a ios be ween a wo kpiece o a-
ion equency and an oscilla ion equency (
o
/
osc
) o 0.5, wi h his being he ampli ude
o hal o he eed pe e olu ion.
Rega ding he p ac ical achie emen o he ool mo ion, Os wald designed a mechani-
cal appa a us composed o a lexible ool in he eed di ec ion, which eached an oscilla ion
equency o 50 Hz and an ampli ude o 1.12 mm. Due o he limi ed applicabili y, Skel-
on [
8
] p esen ed a hyd aulically ac ua ed de ice capable o eaching 125 Hz o ac ua ion
and enabling he equency o he oscilla ion and he ampli ude o be se independen ly.
In o de o ob ain highe ac ua o equencies, as ool se os (FTS) we e used, which
we e able o p oduce oscilla ions o o e 1 kHz in bandwid h in he eed di ec ion [
9
].
Mechanical de ices we e also used o MAM chip b eaking, as used by he MITIS company
o d illing ope a ions [10].
Apa om he be o emen ioned MAM applica ions, some wo ks used he o di-
na y d i es o he machines o pe o m equi ed oscilla ions o he chip b eakage.
Chhab a e al. [11]
designed a 400 Hz bandwid h linea d i e capable o gene a ing a
linea mo ion wi h supe imposed modula ion in he eed di ec ion, enabling chip b eaking
in d illing ope a ions. Woody e al. [
12
] p oposed a CNC oolpa h-based app oach o b eak
he chips in u ning ope a ions. Al hough chip b eakage was achie ed, he modula ion
was p og ammed by means o ajec o y gene a ion in he CNC p og am, which is alid
o i s implemen a ion a a wo kshop-le el. Acco ding o he p ocess pa ame e s, As a loa
e al. [
13
] analyzed MAM pa ame e s, oscilla ion equency, and ampli ude, espec i ely,
wi h he aim o selec ing he mos app op ia e oscilla ion pa ame e s acco ding o he
machine oscilla ion capabili y and p ocess pa ame e s o hea y-du y e ical u ning
machines. They p oposed a me hodology o cha ac e ize he oscilla ion capabili y o he
machine and o au oma ically selec he F-MAM pa ame e s [14].
The ool wea , su ace oughness, and empe a u e a ia ion gene a ed by he applica-
ion o his chip-b eaking echnique we e also analyzed by di e en au ho s. Smi h e al. [
15
]
concluded ha as MAM in ol es an ai -cu ing phase whe e he ool is cooled down, in
his way, a educ ion in he wea can be ob ained, in compa ison o con en ional u ning.
Mann e al. [
9
] analyzed he chip o ma ion and he bene i s o he modula ion-assis ed
machining, including he ool wea and su ace ex u e, concluding ha he p oduc ion
o sho chips acili a es he each o he coolan o he cu ing edge, esul ing in educed
wea . Gao e al. [
16
,
17
] de eloped a model o he p edic ion o he su ace opog aphy and
he mal e ec s, showing ha MAM can educe he a e age ool empe a u e by 30%, com-
pa ed o con en ional machining. Howe e , he be o emen ioned MAM applica ions we e
conduc ed in small-size la hes wi h ex emely low chip loads. The e o e, he conclusions
may no be ex apola ed o hea y-du y machining.
Finally, al hough he modula ion o he ool pa h in he eed di ec ion is a powe ul
ool o chip b eaking, i canno be applied o h eads machining. The main di e ence o
J. Manu . Ma e . P ocess. 2024,8, 167 3 o 14
h eading ope a ions is ha he ool does no encoun e he same ma e ial su ace om he
p e ious e olu ion. Speci ically, as he eed pe e olu ion o he ope a ion is equal o he
h ead pi ch, he e is no o e lapping wi h he p e ious e olu ion.
As an answe o his limi a ion, Be glind e al. [
18
] p oposed a a ia ion in he dep h
o cu di ec ion (D-MAM) o h eading ope a ions. This modula ion was ca ied ou
by means o he machine’s o dina y d i es h ough modula ed ool pa h p og amming.
The e o e, wo di e en ways o apply MAM ha e been p oposed in li e a u e, bu he
pe o mances o hese echniques ha e no been compa ed.
The p esen pape e alua es and compa es di e en MAM echniques o achie ing
chip b eakage du ing he u ning o low machinabili y ma e ials. Fi s , he indus ial
implemen a ion o MAM echniques is analyzed, iden i ying op imized pa ame e s o
he applica ion o bo h D-MAM and F-MAM echniques on big-diame e pa s. Then,
he e alua ion o he pe o mances o such echniques in compa ison o con en ional
u ning is ca ied ou on 17-4 PH s ainless s eel in e ms o chip o ma ion, ool wea , and
su ace oughness. Resul s indica e ha , in con as o some wo ks in he bibliog aphy [
9
],
bo h MAM echniques e alua ed educe ool li e in compa ison o con en ional u ning,
especially he F-MAM echnique. Mo eo e , signi ican ly highe su ace oughness alues
a e achie ed wi h his las echnique in compa ison o he con en ional and D-MAM
echniques. Finally, he conclusions o he p esen ed wo k a e d awn, indica ing u he
esea ch lines o he applica ion o MAM echniques.
2. Modula ion-Assis ed Machining
The chip-b eaking me hods used in he p esen wo k a e based on nulli ying he
unde o med chip hickness on he cu ing ools, hanks o he ha monic modula ion o
he ool pa hs. Conside ing he kinema ics o cylinde u ning ope a ions, he modu-
la ion o he ool pa h can be gene a ed ei he in he eed di ec ion (F-MAM) o in he
dep h o cu di ec ion (D-MAM), as shown in Figu e 1. The implemen a ion o ha monic
modula ions in bo h he axial and adial di ec ions using he machine d i es is shown in
Sec ions 2.1 and 2.2, espec i ely.
J. Manu . Ma e . P ocess. 2024, 8, 167 3 o 14
empe a u e by 30%, compa ed o con en ional machining. Howe e , he be o emen-
ioned MAM applica ions we e conduc ed in small-size la hes wi h ex emely low chip
loads. The e o e, he conclusions may no be ex apola ed o hea y-du y machining.
Finally, al hough he modula ion o he ool pa h in he eed di ec ion is a powe ul
ool o chip b eaking, i canno be applied o h eads machining. The main diffe ence o
h eading ope a ions is ha he ool does no encoun e he same ma e ial su ace om
he p e ious e olu ion. Speci ically, as he eed pe e olu ion o he ope a ion is equal
o he h ead pi ch, he e is no o e lapping wi h he p e ious e olu ion.
As an answe o his limi a ion, Be glind e al. [18] p oposed a a ia ion in he dep h
o cu di ec ion (D-MAM) o h eading ope a ions. This modula ion was ca ied ou by
means o he machine’s o dina y d i es h ough modula ed ool pa h p og amming.
The e o e, wo diffe en ways o apply MAM ha e been p oposed in li e a u e, bu he
pe o mances o hese echniques ha e no been compa ed.
The p esen pape e alua es and compa es diffe en MAM echniques o achie ing
chip b eakage du ing he u ning o low machinabili y ma e ials. Fi s , he indus ial im-
plemen a ion o MAM echniques is analyzed, iden i ying op imized pa ame e s o he
applica ion o bo h D-MAM and F-MAM echniques on big-diame e pa s. Then, he e al-
ua ion o he pe o mances o such echniques in compa ison o con en ional u ning is
ca ied ou on 17-4 PH s ainless s eel in e ms o chip o ma ion, ool wea , and su ace
oughness. Resul s indica e ha , in con as o some wo ks in he bibliog aphy [9], bo h
MAM echniques e alua ed educe ool li e in compa ison o con en ional u ning, espe-
cially he F-MAM echnique. Mo eo e , signi ican ly highe su ace oughness alues a e
achie ed wi h his las echnique in compa ison o he con en ional and D-MAM ech-
niques. Finally, he conclusions o he p esen ed wo k a e d awn, indica ing u he e-
sea ch lines o he applica ion o MAM echniques.
2. Modula ion-Assis ed Machining
The chip-b eaking me hods used in he p esen wo k a e based on nulli ying he un-
de o med chip hickness on he cu ing ools, hanks o he ha monic modula ion o he
ool pa hs. Conside ing he kinema ics o cylinde u ning ope a ions, he modula ion o
he ool pa h can be gene a ed ei he in he eed di ec ion (F-MAM) o in he dep h o cu
di ec ion (D-MAM), as shown in Figu e 1. The implemen a ion o ha monic modula ions
in bo h he axial and adial di ec ions using he machine d i es is shown in Sec ion 2.1
and Sec ion 2.2, espec i ely.
Figu e 1. Diag am o a cylinde u ning ope a ion and di ec ions o he ha monic modula ion.
2.1. Modula ion-Assis ed Machining h ough Feed Va ia ion (F-MAM)
To gene a e a a iable eed u ning ool pa h, a ha monic ib a ion is added o he
ool ajec o y in he axial di ec ion o he pa . The ha monic oscilla ion applied on he
ool gene a es an in e e ence be ween successi e passes in he axial di ec ion. Depending
on he equency ela ionship be ween he spindle o a ion and he equency o he
Figu e 1. Diag am o a cylinde u ning ope a ion and di ec ions o he ha monic modula ion.
2.1. Modula ion-Assis ed Machining h ough Feed Va ia ion (F-MAM)
To gene a e a a iable eed u ning ool pa h, a ha monic ib a ion is added o he ool
ajec o y in he axial di ec ion o he pa . The ha monic oscilla ion applied on he ool
gene a es an in e e ence be ween successi e passes in he axial di ec ion. Depending on
he equency ela ionship be ween he spindle o a ion and he equency o he ha monic
modula ion, his in e e ence can nulli y he chip load when he axial maximum om
a p e ious pass and he axial minimum o he p esen pass coincide o in e sec . In
o de o achie e his poin wi h he minimum ampli ude, he equency ela ionship mus
co espond o an in ege +0.5 (i.e., 0.5, 1.5, o 2.5) [
7
]. Figu e 2shows he ool pa hs o a
con en ional u ning and o an F-MAM, wi h an oscilla ion equency ela ionship o 1.5.
J. Manu . Ma e . P ocess. 2024,8, 167 4 o 14
J. Manu . Ma e . P ocess. 2024, 8, 167 4 o 14
ha monic modula ion, his in e e ence can nulli y he chip load when he axial maximum
om a p e ious pass and he axial minimum o he p esen pass coincide o in e sec . In
o de o achie e his poin wi h he minimum ampli ude, he equency ela ionship mus
co espond o an in ege +0.5 (i.e., 0.5, 1.5, o 2.5) [7]. Figu e 2 shows he ool pa hs o a
con en ional u ning and o an F-MAM, wi h an oscilla ion equency ela ionship o 1.5.
Figu e 2. Tool pa h when applying an F-MAM u ning in compa ison o con en ional u ning.
Addi ionally, he ha monic modi ica ion o he ool eed enables he o al ma e ial
emo al a e (MRR) o be kep , in compa ison o a con en ional u ning. Howe e , he
unde o med chip hickness on he ool a ies om ze o o double he nominal eed pe
e olu ion (𝑓) alue, which gene a es oscilla ions on he chip load on he ool. Figu e 3a
shows he chip load calcula ed o bo h con en ional u ning and he F-MAM ope a ion
wi h a dep h o cu (𝑎 o 0.5 mm and a eed pe e olu ion (𝑓 o 0.15 mm/ e . Fo a
con en ional u ning ope a ion, he chip load g ows as he ool comple ely en e s he pa ,
eaching he nominal alue o 0.075 mm
2
, and dec eases down o ze o as he ool exis s in
he pa . In he F-MAM u ning ope a ion, he chip load ollows a simila pa e n, bu i s
alue oscilla es om ze o o double he alue o con en ional u ning along he en i e
u ning p ocess. In his way, as he eed pe e olu ion is doubled, he maximum p essu e
is also doubled in he same diffe en ial elemen o he cu ing edge (Figu e 3b).
Figu e 3. (a) Chip load alues (𝑓
/𝑓
= 1) and (b) p essu e a ia ions in he cu ing edge o con-
en ional (black a ows) and F-MAM ( ed a ows) u nings.
In p e ious wo ks [13,14], a me hod o e alua e he machine oscilla ion capabili y
was in oduced, oge he wi h a p ocedu e o he au oma ic selec ion o he oscilla ion
pa ame e s when applying a a iable eed u ning ope a ion. The p esen wo k ollows
his app oach o he applica ion o he F-MAM echnique du ing he expe imen al anal-
ysis (Sec ion 3).
Figu e 2. Tool pa h when applying an F-MAM u ning in compa ison o con en ional u ning.
Addi ionally, he ha monic modi ica ion o he ool eed enables he o al ma e ial
emo al a e (MRR) o be kep , in compa ison o a con en ional u ning. Howe e , he
unde o med chip hickness on he ool a ies om ze o o double he nominal eed pe
e olu ion (
) alue, which gene a es oscilla ions on he chip load on he ool. Figu e 3a
shows he chip load calcula ed o bo h con en ional u ning and he F-MAM ope a ion
wi h a dep h o cu (
ap)
o 0.5 mm and a eed pe e olu ion (
)
o 0.15 mm/ e . Fo a
con en ional u ning ope a ion, he chip load g ows as he ool comple ely en e s he pa ,
eaching he nominal alue o 0.075 mm
2
, and dec eases down o ze o as he ool exis s
in he pa . In he F-MAM u ning ope a ion, he chip load ollows a simila pa e n, bu
i s alue oscilla es om ze o o double he alue o con en ional u ning along he en i e
u ning p ocess. In his way, as he eed pe e olu ion is doubled, he maximum p essu e
is also doubled in he same di e en ial elemen o he cu ing edge (Figu e 3b).
J. Manu . Ma e . P ocess. 2024, 8, 167 4 o 14
ha monic modula ion, his in e e ence can nulli y he chip load when he axial maximum
om a p e ious pass and he axial minimum o he p esen pass coincide o in e sec . In
o de o achie e his poin wi h he minimum ampli ude, he equency ela ionship mus
co espond o an in ege +0.5 (i.e., 0.5, 1.5, o 2.5) [7]. Figu e 2 shows he ool pa hs o a
con en ional u ning and o an F-MAM, wi h an oscilla ion equency ela ionship o 1.5.
Figu e 2. Tool pa h when applying an F-MAM u ning in compa ison o con en ional u ning.
Addi ionally, he ha monic modi ica ion o he ool eed enables he o al ma e ial
emo al a e (MRR) o be kep , in compa ison o a con en ional u ning. Howe e , he
unde o med chip hickness on he ool a ies om ze o o double he nominal eed pe
e olu ion (𝑓) alue, which gene a es oscilla ions on he chip load on he ool. Figu e 3a
shows he chip load calcula ed o bo h con en ional u ning and he F-MAM ope a ion
wi h a dep h o cu (𝑎 o 0.5 mm and a eed pe e olu ion (𝑓 o 0.15 mm/ e . Fo a
con en ional u ning ope a ion, he chip load g ows as he ool comple ely en e s he pa ,
eaching he nominal alue o 0.075 mm
2
, and dec eases down o ze o as he ool exis s in
he pa . In he F-MAM u ning ope a ion, he chip load ollows a simila pa e n, bu i s
alue oscilla es om ze o o double he alue o con en ional u ning along he en i e
u ning p ocess. In his way, as he eed pe e olu ion is doubled, he maximum p essu e
is also doubled in he same diffe en ial elemen o he cu ing edge (Figu e 3b).
Figu e 3. (a) Chip load alues (𝑓
/𝑓
= 1) and (b) p essu e a ia ions in he cu ing edge o con-
en ional (black a ows) and F-MAM ( ed a ows) u nings.
In p e ious wo ks [13,14], a me hod o e alua e he machine oscilla ion capabili y
was in oduced, oge he wi h a p ocedu e o he au oma ic selec ion o he oscilla ion
pa ame e s when applying a a iable eed u ning ope a ion. The p esen wo k ollows
his app oach o he applica ion o he F-MAM echnique du ing he expe imen al anal-
ysis (Sec ion 3).
Figu e 3. (a) Chip load alues (
osc
/
o
= 1) and (b) p essu e a ia ions in he cu ing edge o
con en ional (black a ows) and F-MAM ( ed a ows) u nings.
In p e ious wo ks [
13
,
14
], a me hod o e alua e he machine oscilla ion capabil-
i y was in oduced, oge he wi h a p ocedu e o he au oma ic selec ion o he oscil-
la ion pa ame e s when applying a a iable eed u ning ope a ion. The p esen wo k
ollows his app oach o he applica ion o he F-MAM echnique du ing he expe imen al
analysis (Sec ion 3).
2.2. Modula ion-Assis ed Machining h ough Dep h o Cu Va ia ion (D-MAM)
When he dep h o cu di ec ion MAM is applied in longi udinal u ning ope a ions,
an oscilla ion is applied o e he adial di ec ion o he wo kpiece, c ea ing a a ia ion in
he ac ual diame e machined by he ool (Figu e 4). This way, he ool lea es he wo kpiece
a some ci cum e en ial loca ions, c ea ing discon inuous chips. Ne e heless, his s a egy
J. Manu . Ma e . P ocess. 2024,8, 167 5 o 14
does no gene a e a cylind ical shape o , a leas , a cylind ical shape coaxial o he s a ing
cylind ical pa . The e o e, a second pass wi hou modula ion is equi ed o gene a e a
inal coaxial cylind ical shape a e he execu ion o an ini ial a iable pass.
J. Manu . Ma e . P ocess. 2024, 8, 167 5 o 14
2.2. Modula ion-Assis ed Machining h ough Dep h o Cu Va ia ion (D-MAM)
When he dep h o cu di ec ion MAM is applied in longi udinal u ning ope a ions,
an oscilla ion is applied o e he adial di ec ion o he wo kpiece, c ea ing a a ia ion in
he ac ual diame e machined by he ool (Figu e 4). This way, he ool lea es he wo k-
piece a some ci cum e en ial loca ions, c ea ing discon inuous chips. Ne e heless, his
s a egy does no gene a e a cylind ical shape o , a leas , a cylind ical shape coaxial o he
s a ing cylind ical pa . The e o e, a second pass wi hou modula ion is equi ed o gen-
e a e a inal coaxial cylind ical shape a e he execu ion o an ini ial a iable pass.
Figu e 4. Tool pa h when applying a D-MAM in compa ison o con en ional u ning (𝑓
/𝑓
=
1).
The leng h o such disc e e chips is dependen upon he oscilla ion equency (𝑓).
When his equency is equal o he wo kpiece o a ional equency (𝑓), he leng h o
he chip will be he same as he pe ime e o he pa , p oducing an eccen ic pa . Highe
oscilla ion equencies will gene a e sho e chips.
In o de o compa e he D-MAM s a egy wi h con en ional u ning, he ma e ial
emo al a e (MRR) mus be kep cons an . The e o e, he maximum dep h o cu alue in
he D-MAM mus be double ha used du ing con en ional u ning. This is shown in Fig-
u e 5, whe e he s aigh black and blue lines a e he cumula i e dep hs o cu o he i s
and second con en ional (as well as F-MAM) machining ope a ions, espec i ely, while
he ed and g een sinusoidal lines ep esen he dep hs o cu o he i s and second D-
MAM p ocesses, espec i ely. I mus be highligh ed ha only he i s D-MAM machin-
ing has a modula ed pa h, while he second one has a con en ional ajec o y. The non-
ci cum e en ial shape gene a ed in he i s pass makes his second pass gene a e discon-
inuous chips wi h a con en ional u ning ajec o y. This second con en ional pass also
has a a iable chip hickness, due o he effec o he i s non-con en ional D-MAM pass.
No ice ha he sum o he dep h o cu s o he successi e cu s in a ce ain angula cu is
cons an (see Figu e 5).
In he case o he a iable dep h o cu MAM, he dimensionless oscilla ion equency
(𝑓/𝑓) mus be an in ege (i.e., 1, 2, 3, …). In case o an une en ela ionship be ween
bo h equencies, while discon inuous chips will be p oduced, an in e e ence is c ea ed
be ween ool ajec o ies a diffe en axial loca ions. Figu e 6 shows he X–Y iew o he
a iable dep h o cu ajec o ies o dimensionless oscilla ion (𝑓/𝑓) ela ions o 3 and
1.5. As i can be seen, in he case o an in ege ela ionship, he adial loca ion o he ool
ajec o y o a ci cum e en ial posi ion o he pa is kep cons an . In he case o an une-
en ela ionship, his adial loca ion is a iable. This leads o in e e ences be ween he
ool and he ma e ial le by passes in diffe en axial loca ions, which makes he chip load
on he ool inc ease o e he nominal alue. In addi ion, he alue o such an in ege mus
be de ined acco ding o he machine’s oscilla ion capaci y and by selec ing he highes
possible alue o p oduce he sho es possible chips.
Figu e 4. Tool pa h when applying a D-MAM in compa ison o con en ional u ning ( osc/ o = 1).
The leng h o such disc e e chips is dependen upon he oscilla ion equency (
osc
).
When his equency is equal o he wo kpiece o a ional equency (
o
), he leng h o he
chip will be he same as he pe ime e o he pa , p oducing an eccen ic pa . Highe
oscilla ion equencies will gene a e sho e chips.
In o de o compa e he D-MAM s a egy wi h con en ional u ning, he ma e ial
emo al a e (MRR) mus be kep cons an . The e o e, he maximum dep h o cu alue
in he D-MAM mus be double ha used du ing con en ional u ning. This is shown
in Figu e 5, whe e he s aigh black and blue lines a e he cumula i e dep hs o cu o
he i s and second con en ional (as well as F-MAM) machining ope a ions, espec i ely,
while he ed and g een sinusoidal lines ep esen he dep hs o cu o he i s and
second D-MAM p ocesses, espec i ely. I mus be highligh ed ha only he i s D-MAM
machining has a modula ed pa h, while he second one has a con en ional ajec o y. The
non-ci cum e en ial shape gene a ed in he i s pass makes his second pass gene a e
discon inuous chips wi h a con en ional u ning ajec o y. This second con en ional pass
also has a a iable chip hickness, due o he e ec o he i s non-con en ional D-MAM
pass. No ice ha he sum o he dep h o cu s o he successi e cu s in a ce ain angula cu
is cons an (see Figu e 5).
J. Manu . Ma e . P ocess. 2024, 8, 167 6 o 14
Figu e 5. Dep h o cu alues o wo con en ional and a iable dep h o cu passes, depending on
he pa ci cum e en ial angle, o a dimensionless oscilla ion a io equal o 1.
Figu e 6. Tool ajec o ies o he D-MAM p ocess wi h diffe en equency ela ions: (a) 𝑓
/𝑓
=
3, and (b) 𝑓
/𝑓
= 1.5.
The applica ion o D-MAM o achie e a discon inuous chip equi es a speci ic oscil-
la ion equency ha can be calcula ed om he wo kpiece diame e and he cu ing
speed. In addi ion, oscilla ion equency is in e sely p opo ional o he wo kpiece diam-
e e , so in small diame e pa s, he oscilla ion equency inc eases. In his way, o apply
he MAM echnique in small pa s (D < 50 mm), linea mo o s o FTSs a e gene ally
needed o each he equi ed equency. Howe e , when he size o he pa app oaches
he egion o hea y-du y indus ial applica ions (D > 1000 mm), he ypical d i es used in
la ge-size machine ools can each he necessa y equency o gene a e discon inuous
chips. The e o e, when la ge-diame e wo kpieces a e p oduced, bo h MAM me hods can
be applied using he o dina y d i es o he machine, no ma e he ma e ial being cu .
Figu e 7a shows he calcula ed chip load o a D-MAM ajec o y when using a 0.15
mm/ e eed pe e olu ion (𝑓) and a a iable dep h o cu (𝑎) o 0–1 mm. As i can be
seen, he chip load o he case o an in ege equency ela ionship (𝑓/𝑓 = 1) is a ia-
ble om ze o o double he chip load o a con en ional u ning ope a ion (0.075 mm
2
). In
he case o an une en, dimensionless (𝑓/𝑓 = 1.5) oscilla ion equency, he chip load
can ake alues up o ou imes he chip load o con en ional u ning, which can lead o
excessi e loads on he cu ing ool and gene a e i s b eakage. Acco ding o he p essu e
gene a ed in he cu ing edge when he D-MAM echnique is applied, al hough a a ia ion
Figu e 5. Dep h o cu alues o wo con en ional and a iable dep h o cu passes, depending on
he pa ci cum e en ial angle, o a dimensionless oscilla ion a io equal o 1.
J. Manu . Ma e . P ocess. 2024,8, 167 6 o 14
In he case o he a iable dep h o cu MAM, he dimensionless oscilla ion equency
(
osc
/
o
) mus be an in ege (i.e., 1, 2, 3,
. . .
). In case o an une en ela ionship be ween
bo h equencies, while discon inuous chips will be p oduced, an in e e ence is c ea ed
be ween ool ajec o ies a di e en axial loca ions. Figu e 6shows he X–Y iew o he
a iable dep h o cu ajec o ies o dimensionless oscilla ion (
osc
/
o
) ela ions o 3 and
1.5. As i can be seen, in he case o an in ege ela ionship, he adial loca ion o he ool
ajec o y o a ci cum e en ial posi ion o he pa is kep cons an . In he case o an une en
ela ionship, his adial loca ion is a iable. This leads o in e e ences be ween he ool and
he ma e ial le by passes in di e en axial loca ions, which makes he chip load on he ool
inc ease o e he nominal alue. In addi ion, he alue o such an in ege mus be de ined
acco ding o he machine’s oscilla ion capaci y and by selec ing he highes possible alue
o p oduce he sho es possible chips.
J. Manu . Ma e . P ocess. 2024, 8, 167 6 o 14
Figu e 5. Dep h o cu alues o wo con en ional and a iable dep h o cu passes, depending on
he pa ci cum e en ial angle, o a dimensionless oscilla ion a io equal o 1.
Figu e 6. Tool ajec o ies o he D-MAM p ocess wi h diffe en equency ela ions: (a) 𝑓
/𝑓
=
3, and (b) 𝑓
/𝑓
= 1.5.
The applica ion o D-MAM o achie e a discon inuous chip equi es a speci ic oscil-
la ion equency ha can be calcula ed om he wo kpiece diame e and he cu ing
speed. In addi ion, oscilla ion equency is in e sely p opo ional o he wo kpiece diam-
e e , so in small diame e pa s, he oscilla ion equency inc eases. In his way, o apply
he MAM echnique in small pa s (D < 50 mm), linea mo o s o FTSs a e gene ally
needed o each he equi ed equency. Howe e , when he size o he pa app oaches
he egion o hea y-du y indus ial applica ions (D > 1000 mm), he ypical d i es used in
la ge-size machine ools can each he necessa y equency o gene a e discon inuous
chips. The e o e, when la ge-diame e wo kpieces a e p oduced, bo h MAM me hods can
be applied using he o dina y d i es o he machine, no ma e he ma e ial being cu .
Figu e 7a shows he calcula ed chip load o a D-MAM ajec o y when using a 0.15
mm/ e eed pe e olu ion (𝑓) and a a iable dep h o cu (𝑎) o 0–1 mm. As i can be
seen, he chip load o he case o an in ege equency ela ionship (𝑓/𝑓 = 1) is a ia-
ble om ze o o double he chip load o a con en ional u ning ope a ion (0.075 mm
2
). In
he case o an une en, dimensionless (𝑓/𝑓 = 1.5) oscilla ion equency, he chip load
can ake alues up o ou imes he chip load o con en ional u ning, which can lead o
excessi e loads on he cu ing ool and gene a e i s b eakage. Acco ding o he p essu e
gene a ed in he cu ing edge when he D-MAM echnique is applied, al hough a a ia ion
Figu e 6. Tool ajec o ies o he D-MAM p ocess wi h di e en equency ela ions: (a)
osc
/
o
= 3,
and (b) osc/ o = 1.5.
The applica ion o D-MAM o achie e a discon inuous chip equi es a speci ic oscilla-
ion equency ha can be calcula ed om he wo kpiece diame e and he cu ing speed.
In addi ion, oscilla ion equency is in e sely p opo ional o he wo kpiece diame e , so in
small diame e pa s, he oscilla ion equency inc eases. In his way, o apply he MAM
echnique in small pa s (D < 50 mm), linea mo o s o FTSs a e gene ally needed o each
he equi ed equency. Howe e , when he size o he pa app oaches he egion o hea y-
du y indus ial applica ions (D > 1000 mm), he ypical d i es used in la ge-size machine
ools can each he necessa y equency o gene a e discon inuous chips. The e o e, when
la ge-diame e wo kpieces a e p oduced, bo h MAM me hods can be applied using he
o dina y d i es o he machine, no ma e he ma e ial being cu .
Figu e 7a shows he calcula ed chip load o a D-MAM ajec o y when using a
0.15 mm/ e eed pe e olu ion (
) and a a iable dep h o cu (
ap
) o 0–1 mm. As i
can be seen, he chip load o he case o an in ege equency ela ionship (
osc
/
o
= 1) is
a iable om ze o o double he chip load o a con en ional u ning ope a ion
(0.075 mm2)
.
In he case o an une en, dimensionless (
osc
/
o
= 1.5) oscilla ion equency, he chip load
can ake alues up o ou imes he chip load o con en ional u ning, which can lead o
excessi e loads on he cu ing ool and gene a e i s b eakage. Acco ding o he p essu e
gene a ed in he cu ing edge when he D-MAM echnique is applied, al hough a a ia ion
in he dep h o cu is gene a ed, he maximum p essu e on each di e en ial elemen o
he cu ing edge has he same alue as in he con en ional case (black and ed a ows in
Figu e 7b).
J. Manu . Ma e . P ocess. 2024,8, 167 7 o 14
J. Manu . Ma e . P ocess. 2024, 8, 167 7 o 14
in he dep h o cu is gene a ed, he maximum p essu e on each diffe en ial elemen o he
cu ing edge has he same alue as in he con en ional case (black and ed a ows in Figu e
7b).
Figu e 7. (a) Chip load alues o a con en ional u ning and a D-MAM wi h ela ions o 𝑓
/𝑓
= 1.5 and 𝑓
/𝑓
= 1. (b) P essu e a ia ions in he cu ing edge o con en ional (black a ows)
and D-MAM u nings (addi ional load ep esen ed by ed a ows).
Rega ding he p ac ical implemen a ion o he dep h o cu di ec ion MAM, oscilla-
o y ajec o ies a e p og ammed in he NC code, ollowing he nex ela ionship:
𝑋𝑡=𝐷+2𝑎 2𝑎cos
𝑓
𝑓
2𝜋𝑁
60 𝑡 (1)
In Equa ion (1), 𝑋𝑡 is he diame al posi ion o he ool, 𝐷 is he diame e o he
wo kpiece, 𝑎 is he dep h o cu and 𝑁 is he spindle speed. In o de o a oid synch o-
niza ion issues be ween axes, he spindle speed is kep cons an du ing he es s.
Howe e , he oscilla ion o he ool ajec o y in he dep h o cu di ec ion (𝑋) gen-
e a es longe ool pa h leng hs han in con en ional u ning o a wo kpiece e olu ion.
Coupled wi h he diffe en ial displacemen applied in he eed di ec ion (𝑑𝑍), he mo ion
in he 𝑋 di ec ion gene a es an addi ional 𝑑𝑋 displacemen ha inc eases he ac ual
ool pa h leng h (Figu e 8).
Figu e 8. Tool pa h o he pa e olu ion when applying D-MAM. Diffe en ial displacemen be-
ween ed do s highligh ed by black lines.
Figu e 7. (a) Chip load alues o a con en ional u ning and a D-MAM wi h ela ions o
osc/ o = 1.5 and osc/ o = 1
. (b) P essu e a ia ions in he cu ing edge o con en ional (black
a ows) and D-MAM u nings (addi ional load ep esen ed by ed a ows).
Rega ding he p ac ical implemen a ion o he dep h o cu di ec ion MAM, oscilla o y
ajec o ies a e p og ammed in he NC code, ollowing he nex ela ionship:
XD( )=D+2ap−2apcos osc
o
2πN
60 (1)
In Equa ion (1),
XD( )
is he diame al posi ion o he ool,
D
is he diame e o
he wo kpiece,
ap
is he dep h o cu and
N
is he spindle speed. In o de o a oid
synch oniza ion issues be ween axes, he spindle speed is kep cons an du ing he es s.
Howe e , he oscilla ion o he ool ajec o y in he dep h o cu di ec ion (
XD
)
gene a es longe ool pa h leng hs han in con en ional u ning o a wo kpiece e olu ion.
Coupled wi h he di e en ial displacemen applied in he eed di ec ion (
dZ
), he mo ion
in he
XD
di ec ion gene a es an addi ional
dXD
displacemen ha inc eases he ac ual ool
pa h leng h (Figu e 8).
J. Manu . Ma e . P ocess. 2024, 8, 167 7 o 14
in he dep h o cu is gene a ed, he maximum p essu e on each diffe en ial elemen o he
cu ing edge has he same alue as in he con en ional case (black and ed a ows in Figu e
7b).
Figu e 7. (a) Chip load alues o a con en ional u ning and a D-MAM wi h ela ions o 𝑓
/𝑓
= 1.5 and 𝑓
/𝑓
= 1. (b) P essu e a ia ions in he cu ing edge o con en ional (black a ows)
and D-MAM u nings (addi ional load ep esen ed by ed a ows).
Rega ding he p ac ical implemen a ion o he dep h o cu di ec ion MAM, oscilla-
o y ajec o ies a e p og ammed in he NC code, ollowing he nex ela ionship:
𝑋𝑡=𝐷+2𝑎 2𝑎cos
𝑓
𝑓
2𝜋𝑁
60 𝑡 (1)
In Equa ion (1), 𝑋𝑡 is he diame al posi ion o he ool, 𝐷 is he diame e o he
wo kpiece, 𝑎 is he dep h o cu and 𝑁 is he spindle speed. In o de o a oid synch o-
niza ion issues be ween axes, he spindle speed is kep cons an du ing he es s.
Howe e , he oscilla ion o he ool ajec o y in he dep h o cu di ec ion (𝑋) gen-
e a es longe ool pa h leng hs han in con en ional u ning o a wo kpiece e olu ion.
Coupled wi h he diffe en ial displacemen applied in he eed di ec ion (𝑑𝑍), he mo ion
in he 𝑋 di ec ion gene a es an addi ional 𝑑𝑋 displacemen ha inc eases he ac ual
ool pa h leng h (Figu e 8).
Figu e 8. Tool pa h o he pa e olu ion when applying D-MAM. Diffe en ial displacemen be-
ween ed do s highligh ed by black lines.
Figu e 8. Tool pa h o he pa e olu ion when applying D-MAM. Di e en ial displacemen be ween
ed do s highligh ed by black lines.
I he p og ammed eed pe e olu ion alue is kep cons an , his longe ool pa h
would gene a e longe machining imes han con en ional u ning, as well as a a iable
unde o med chip hickness on he ool. To a oid such issues, he p og ammed eed mus be
modi ied oo, conside ing he ool mo ions in bo h
Z
and
XD
di ec ions. Fo ha pu pose,
he eed pe e olu ion a each ajec o y loca ion (
ap
) can be calcula ed acco ding o
J. Manu . Ma e . P ocess. 2024,8, 167 8 o 14
Equa ion (2), using he modulus o he eloci y ec o o med by he displacemen s in he
Zand XDdi ec ions.
ap=s 2+4apπsin osc
o
2πN
60 2
(2)
3. Expe imen al Valida ion
In o de o e alua e he pe o mance o he chip-b eaking me hods in compa ison o
con en ional u ning ope a ions, as well as hei impac on ool li e, u ning es s we e
ca ied ou . A 900 mm diame e olled ing made o 17-4 PH p ecipi a ion-ha dened
s ainless s eel in H900 condi ion (45
±
1 HRC) was used as he wo kpiece ma e ial, while
con en ional, oil-based coolan (5% concen a ion) was used as he cu ing luid. Cylinde
u ning es s we e pe o med in a So aluce (FMT-4000,Be ga a, Spain) mul i asking machine
using eed and dep h o cu MAM echniques, as well as con en ional u ning. Table 1
shows he cu ing pa ame e s and ools employed du ing he es s.
Table 1. Cu ing pa ame e s employed du ing he expe imen al es s.
Cu ing Condi ions
Con en ional D-MAM F-MAM
Cu ing speed, Vc [m/min] 200 200 200
Feed pe e olu ion, [mm/ e ] 0.15 0.15 0–0.3
Dep h o cu , ap[mm] 0.5 0–1 0.5
osc/ o [-] - 1 1.5
Remo ed ma e ial, Q [cm3]100, 200, 300, 400, 500
Cu ing ool
Toolholde PCLNL 2525M 12
Inse Sand ik CNMG 120412-MS MP9015
Rega ding he cu ing pa ame e s, he chip load alues we e selec ed based on da a
om he bibliog aphy [
19
]. The cu ing speed was chosen o achie e a ool li e o ap-
p oxima ely 0.5 h in con en ional u ning, he eby a oiding excessi ely long es s. I
should be no ed ha he selec ed inse had a chip-b eake geome y bu could no gen-
e a e chip b eakage du ing con en ional u ning. To allow a ai compa ison be ween
he esul s om each es , hey we e di ided in o di e en passes, keeping he emo ed
ma e ial (Q) cons an o each pass (100 cm
3
). Th ee epe i ions we e pe o med o each
machining s a egy.
Rega ding he oscilla ion pa ame e s, hei selec ion should keep he chip leng h
simila in bo h MAM s a egies o pe o m a ai compa ison. Howe e , F-MAM equi es
oscilla ion equencies ha a e 0.5, 1.5, 2.5
. . .
imes he o a ional equency o b eak he
chips wi h he minimum a ia ion [
13
]. On he con a y, D-MAM equi es oscilla ion
equencies ha a e in ege mul iples o he o a ional equency. The e o e, i is no
possible o achie e simila chip leng hs o he same wo kpiece diame e . Bea ing in
mind machine d i e limi a ions and he high mass o he machine componen s, he lowes
dimensionless oscilla ion equencies o 1.5 and 1 we e selec ed o F-MAM and D-MAM,
espec i ely, o a oid synch oniza ion e o s and o ensu e accu a e MAM oscilla ions.
3.1. Chip Gene a ion
Du ing con en ional cu ing es s, big chip nes s we e gene a ed a ound he cu ing
ool. Figu e 9a shows highligh ed by a yellow ci cle one o hese chip nes s en angled
be ween he pa and he cu ing ool. On he con a y, du ing he use o bo h MAM
echniques, he gene a ion o disc e e-leng h chips was achie ed, lea ing he cu ing zone
ee om chip nes s (Figu e 9b). The chips ob ained o each es we e collec ed o e alua e
he capabili y o he applied modula ion-assis ed machining echniques o imp o e he
J. Manu . Ma e . P ocess. 2024,8, 167 9 o 14
chip con ol, in compa ison o con en ional u ning ope a ions (Figu e 10). As i can be
seen, he condi ions employed du ing he con en ional u ning ope a ion we e unable o
gene a e chip b eakage, leading o long chips. Du ing he execu ion o he machining es s,
such long chips we e olled a ound he pa and he ix u e, gene a ing impac s on he ool,
as well as in he machine head and enclosu e. Mo eo e , he chip nes s s uck in he cu ing
zone would sc a ch he machined su ace du ing he u ning ope a ion.
J. Manu . Ma e . P ocess. 2024, 8, 167 9 o 14
3.1. Chip Gene a ion
Du ing con en ional cu ing es s, big chip nes s we e gene a ed a ound he cu ing
ool. Figu e 9a shows highligh ed by a yellow ci cle one o hese chip nes s en angled be-
ween he pa and he cu ing ool. On he con a y, du ing he use o bo h MAM ech-
niques, he gene a ion o disc e e-leng h chips was achie ed, lea ing he cu ing zone ee
om chip nes s (Figu e 9b). The chips ob ained o each es we e collec ed o e alua e he
capabili y o he applied modula ion-assis ed machining echniques o imp o e he chip
con ol, in compa ison o con en ional u ning ope a ions (Figu e 10). As i can be seen,
he condi ions employed du ing he con en ional u ning ope a ion we e unable o gen-
e a e chip b eakage, leading o long chips. Du ing he execu ion o he machining es s,
such long chips we e olled a ound he pa and he ix u e, gene a ing impac s on he
ool, as well as in he machine head and enclosu e. Mo eo e , he chip nes s s uck in he
cu ing zone would sc a ch he machined su ace du ing he u ning ope a ion.
Figu e 9. Execu ion o machining es s o (a) con en ional u ning whe e a chip nes en angled
be ween he pa and he ool can be seen and (b) F-MAM.
Figu e 10. Examples o chips ob ained du ing (a) con en ional u ning, (b) F-MAM, and (c) D-
MAM.
In he case o MAM, discon inuous chips we e ob ained du ing he eed and dep h
o cu modula ion es s, as shown in Figu e 10b and Figu e 10c, espec i ely. In bo h cases,
he chips showed a iable hicknesses, om hin ends o a s u dy cen e , co esponding
o he a iable chip load gene a ed when applying he MAM echniques. The diffe en
chip leng hs we e ela ed o he op imum oscilla ion pa ame e s, as diffe en 𝑓/𝑓 a-
ios mus be used o chip b eakage in bo h echniques. Wi h he employed a ios, D-MAM
p oduced one chip pe e olu ion, while 1.5 chips we e gene a ed wi h F-MAM.
Figu e 9. Execu ion o machining es s o (a) con en ional u ning whe e a chip nes en angled
be ween he pa and he ool can be seen and (b) F-MAM.
J. Manu . Ma e . P ocess. 2024, 8, 167 9 o 14
3.1. Chip Gene a ion
Du ing con en ional cu ing es s, big chip nes s we e gene a ed a ound he cu ing
ool. Figu e 9a shows highligh ed by a yellow ci cle one o hese chip nes s en angled be-
ween he pa and he cu ing ool. On he con a y, du ing he use o bo h MAM ech-
niques, he gene a ion o disc e e-leng h chips was achie ed, lea ing he cu ing zone ee
om chip nes s (Figu e 9b). The chips ob ained o each es we e collec ed o e alua e he
capabili y o he applied modula ion-assis ed machining echniques o imp o e he chip
con ol, in compa ison o con en ional u ning ope a ions (Figu e 10). As i can be seen,
he condi ions employed du ing he con en ional u ning ope a ion we e unable o gen-
e a e chip b eakage, leading o long chips. Du ing he execu ion o he machining es s,
such long chips we e olled a ound he pa and he ix u e, gene a ing impac s on he
ool, as well as in he machine head and enclosu e. Mo eo e , he chip nes s s uck in he
cu ing zone would sc a ch he machined su ace du ing he u ning ope a ion.
Figu e 9. Execu ion o machining es s o (a) con en ional u ning whe e a chip nes en angled
be ween he pa and he ool can be seen and (b) F-MAM.
Figu e 10. Examples o chips ob ained du ing (a) con en ional u ning, (b) F-MAM, and (c) D-
MAM.
In he case o MAM, discon inuous chips we e ob ained du ing he eed and dep h
o cu modula ion es s, as shown in Figu e 10b and Figu e 10c, espec i ely. In bo h cases,
he chips showed a iable hicknesses, om hin ends o a s u dy cen e , co esponding
o he a iable chip load gene a ed when applying he MAM echniques. The diffe en
chip leng hs we e ela ed o he op imum oscilla ion pa ame e s, as diffe en 𝑓/𝑓 a-
ios mus be used o chip b eakage in bo h echniques. Wi h he employed a ios, D-MAM
p oduced one chip pe e olu ion, while 1.5 chips we e gene a ed wi h F-MAM.
Figu e 10. Examples o chips ob ained du ing (a) con en ional u ning, (b) F-MAM, and (c) D-MAM.
In he case o MAM, discon inuous chips we e ob ained du ing he eed and dep h
o cu modula ion es s, as shown in Figu es 10b and 10c, espec i ely. In bo h cases, he
chips showed a iable hicknesses, om hin ends o a s u dy cen e , co esponding o
he a iable chip load gene a ed when applying he MAM echniques. The di e en chip
leng hs we e ela ed o he op imum oscilla ion pa ame e s, as di e en
osc
/
o
a ios
mus be used o chip b eakage in bo h echniques. Wi h he employed a ios, D-MAM
p oduced one chip pe e olu ion, while 1.5 chips we e gene a ed wi h F-MAM.
While signi ican ly lowe -sized chips we e epo ed in he bibliog aphy [
4
,
9
,
18
], hose
esul s we e ob ained wi h low-mass and high-dynamic Swiss- ype u ning cen e s. The
chip leng hs ob ained in he p esen wo k, adap ing he MAM echniques o he oscilla ion
capabili ies o hea y-du y machines, we e adequa e o a oid he issues ela ed o chip
en anglemen and con ol indica ed abo e.
