applied
sciences
A icle
Expe imen al S udy o he Volume ic E o E ec on
he Resul ing Wo king Accu acy—Roundness
Michal Holub 1,* , Robe Janko ych 1, Jan Ve iska 1, Jan S amek 1, Pe Blecha 1, Jan Smolik 2
and Pe Hein ich 3
1Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, CZ 601 90 B no, Czech Republic;
[email p o ec ed].cz (R.J.); [email p o ec ed].cz (J.V.); [email p o ec ed].cz (J.S.);
[email p o ec ed].cz (P.B.)
2Facul y o Mechanical Enginee ing, Czech Technical Uni e si y in P ague,
CZ 166 36 P ague, Czech Republic; [email p o ec ed]
3KOVOSVIT MAS Machine Tools, 391 02 Sezimo o Us i, Czech Republic; [email p o ec ed]
*Co espondence: Michal.Holub@ u b .cz
Recei ed: 4 Augus 2020; Accep ed: 4 Sep embe 2020; Published: 8 Sep embe 2020


Abs ac :
Cu en ly, a ious ypes o so wa e compensa ions a e applied o machine ools. Thei aim
is o inc ease he wo king accu acy o he ools. The imp o emen in wo king accu acy is hen u he
assessed acco ding o he inc ease in he dimensional and shape accu acy o he su ace quali y o he
wo kpiece. This publica ion desc ibes he e ec s o he olume ic accu acy o a machine ool on he
wo king accu acy o a wo kpiece, whe e o al oundness (RON ) is e alua ed in mul iple cu s. In he
expe imen , wo es wo kpieces a e manu ac u ed on a h ee-axis milling machining cen e. The i s
is made using a s anda d machine se up while he second wi h ac i a ed olume ic compensa ion.
The Lase TRACER sel - acking lase in e e ome e is used o compensa e o olume ic accu acy.
In he second pa , e i ica ion measu emen s a e pe o med wi h a Ballba , whe e oundness e o
is e alua ed acco ding o ISO 230-4. Then wo es wo kpieces a e machined, and, in he las pa ,
measu emen is pe o med on Taly ond 595S oundness measu ing equipmen . Finally, he esul s a e
analysed and he dependence be ween he olume ic accu acy, he ci cula i y e o o he machine
and he wo king accu acy o he CNC machine ool is es ablished, ep esen ed by he RON o he
wo kpiece. This pape p esen s new and unpublished ela ions be ween he olume ic accu acy o
he machine ool and he RON o he wo kpiece.
Keywo ds:
machine ool e o ; wo kpiece quali y; machining accu acy; olume ic e o ;
ci cula i y; oundness
1. In oduc ion
The inc ease o he p oduc ion accu acy o machine ools is a con inuous p ocess wi h he
in ol emen o all manu ac u e s. P oduc ion accu acy is a machine ea u e ha is also an indica o o
compe i i eness; i s con inuous imp o emen is also equi ed by he machine use s hemsel es.
The pe cen age o quasi-s a ic e o s and he esul ing accu acy o he h ee-axis machine ool was
desc ibed in 2000 by Ramesh [
1
]. He e, he pe cen age was 60–70%. Subsequen ly, Iba aki expanded
his hypo hesis in his 2010 publica ion [
2
] wi h up o 80% o i e-axis machine ools. The inc ease in
he p opo ion o quasi-s a ic e o s is caused by he kinema ic pai o o a y axes o i e-axis machines.
The e a e wo op ions o ensu e high geome ic accu acy. The ime-consuming and mo e expensi e
op ion uses a mechanically adjus ed machine, i.e., no so wa e compensa ion. This op ion is o e ed by
machine manu ac u e s, especially o hei special machines, which a e supplied o indus ies wi h
ex emely high equi emen s o long- e m dimensional s abili y. Ano he op ion is he use o so wa e
Appl. Sci. 2020,10, 6233; doi:10.3390/app10186233 www.mdpi.com/jou nal/applsci
Appl. Sci. 2020,10, 6233 2 o 18
compensa ion, elimina ing he basic sou ces o machine ool e o s. These sou ces include geome ic,
he mal, dynamic and ool wea e o s. [
3
]. Quasi-s a ic e o s a e de ined as e o s in he ela i e
posi ion o he ool cen e poin (TCP) and he wo kpiece; hese change slowly o e ime. They a e
di ec ly ela ed o he s uc u e o he machine ool i sel and can be di ided in o geome ic, kinema ic
and he mal e o s.
The e a e se e al ways o achie ing he goal o inc easing p oduc ion accu acy o assessing
machine accu acy. These include he use o comme cially a ailable so wa e compensa ions o CNC
machine ools, supplemen ed by new, mo e e ec i e me hodical p ocedu es o measu emen and
e alua ion and he deploymen o new measu emen echnologies. The obus ness o a compensa ion
me hod, wi h espec o he human ac o , is p esen ed in e e ence [
4
]. In e e ence [
5
], he e ec o
olume ic compensa ion on he imp o emen o he geome ic accu acy o a small machining cen e,
by up o 60%, is p esen ed. The inc ease o he olume ic accu acy o a i e-axis machining cen e
using a econ igu able a e ac is p esen ed in [
6
]. The use o acking in e e ome e s o assess 2D
geome ic e o s in luenced by empe a u e change is desc ibed in [
7
]. The u ilisa ion o manu ac u ing
accu acy da a o o a ional e o assessmen is p esen ed in [
8
], linea axis compensa ion p ocedu es in
publica ions [
9
,
10
], he use o he Ballba o machine ool e o assessmen and compensa ion in [
11
], a
comp ehensi e assessmen o measu emen me hods, o e exe ion and hei e ec s on la ge machines
in [
12
] and he use o on-machine ool measu emen in [
13
]. When assessing he e ec s o machine
geome ic e o s on a u u e wo kpiece, i is necessa y o conside all e ec s ha inc ease measu emen
unce ain y and hose ha minimise hese unce ain ies.
Ano he g oup is he de elopmen o new ma hema ical models ha desc ibe he geome y o
he machine, which speci ies he posi ion o he TCP [
8
]. Publica ion [
14
] desc ibes he p inciple o
weigh ed mul ila e a ion and i s in luence on he posi ioning o a poin in he machine’s wo king
space, including i s applica ion o he small machining cen e p esen ed in [
15
]. The da a ob ained
om he measu emen can hen be used as compensa ion alues sen o u he p ocessing o he
CNC p og am om he CAM. A compensa ion algo i hm o educing geome ic e o s by changing
he CNC p og am is published in [
16
]. These a e mos ly designed o basic measu ing de ices ha a e
commonly a ailable on he ma ke and ha e al eady been es ablished in he ield o machine inspec ion
and diagnos ics.
The same is ue o empe a u e models o machine ools and hei compensa ions [
17
], whe e he
he mo-elas ic beha iou o machine ool s uc u es and hei in luence on TCP is desc ibed in [
18
].
This a ea also includes empe a u e measu emen s o machine ools [
19
]. F om publica ion [
20
], i is
ob ious ha i is necessa y o ensu e co ec posi ioning o he empe a u e senso s in o de o ob ain
alid da a o co ec ion o he measu ed da a. He e, his in o ma ion was used o e i y machine
s abili y and o co ec he he mal expansion o machine componen s.
Indi idual measu ing de ices can also be ca ego ised acco ding o he size o he machine ools.
This classi ica ion is di ided in o small, medium and la ge CNC machine ools acco ding o he size
o he wo king space and he loading o he machine om he wo kpiece [
21
]. No all machine
ool sizes can be used wi h all de ices and hey should be selec ed acco ding o he accu acy o he
measu ing equipmen .
Geome ic accu acy is assessed acco ding o ISO 230. These p ocedu es a e usually pa o
e i ica ion when deploying new me hods o compensa ion o machine ools o models o p edic
machine accu acy [
22
]. I is based on he basic me hods o compensa ing o he geome ic e o s o
he illage machines summa ised in publica ion [23]. Ano he s anda d ha can be used o e i y he
accu acy o a machine is he es s based on ISO 230-4 ha mos ly use he Ballba . Publica ion [
24
]
p esen s a me hodology o p edic ing componen accu acy based on ci cula in e pola ion and he FE
model. The use o he Ballba , a measu ing de ice and he ci cula in e pola ion es o he diagnosis
o h ee-axis machine ools is desc ibed in [
25
] and he use o ci cula in e pola ion o measu ing
he geome ic e o s o i e-axis machines is desc ibed in publica ion [
26
]. Roundness e o has no
been imp o ed.
Appl. Sci. 2020,10, 6233 3 o 18
The wo king accu acy o a machine can be e i ied using ISO 10791-7 o he s anda dised
componen [
27
]. This wo kpiece is speci ied o e i y he p oduc ion accu acy o h ee-axis kinema ics
wi h he op ion o assessing se e al dimensional and shape de ia ions. Publica ions [
22
] and [
28
]
desc ibe he e ec o machine load on he posi ion o he o a y axis, as well as he esul ing o ien a ion
e o s. When assessing he geome ic e o s o he machine, i is necessa y o conside he machining
o ces and hea dissipa ion in he machine.
This publica ion is ocused on desc ibing he dependence be ween he olume ic accu acy o
he machine and he esul ing wo king accu acy, assessed on he e o o wo kpiece oundness unde
inishing condi ions o machining. The dependence be ween olume ic accu acy and oundness e o
is desc ibed in publica ion [29], acco ding o ISO 230-4.
The p esen ed expe imen ocuses on he e i ica ion o he co ela ion be ween he olume ic
accu acy o machines and p oduc ion accu acy. In his case, geome ic accu acy is ep esen ed by
olume ic accu acy. The measu emen s o olume ic accu acy a e based on he indi ec me hod,
using he sel -guiding lase in e e ome e Lase TRACER. This me hod is desc ibed, o example,
in [
3
]. In o de o assess he in luence o olume ic accu acy on he esul ing wo king accu acy, i is
impo an o obse e cons an ambien condi ions due o he epea abili y o he p oduc ion o es
wo kpieces. The nega i e e ec o empe a u e on he change in olume ic accu acy is desc ibed
in [
30
]. P oduc ion accu acy is ep esen ed in a es wo kpiece designed o e i y oundness e o . This
is hen e i ied by he Taly ond 595S measu ing de ice. The oundness esul s o he wo kpiece a e hen
compa ed o hose ob ained wi h he ci cula in e pola ion es , acco ding o ISO 230-4. The measu ing
de ice used is he Ballba QC20-w.
2. Expe imen al Se up
2.1. The S a egy o he Expe imen
The expe imen se up is shown in Figu e 1. The expe imen was di ided in o wo pa s. In he i s
pa , a h ee-axis machine ool was measu ed wi h i s basic se up, i.e., wi hou so wa e compensa ion
o he geome ic e o s o he machine. In he second se up, olume ic accu acy was compensa ed
o ; no o he geome ic e o compensa ions we e used. I is necessa y o moni o he su ounding
en i onmen h oughou he measu emen p ocess. Moni o ing was ca ied ou acco ding o he
p ocedu e desc ibed in [20].
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 o 18
The wo king accu acy o a machine can be e i ied using ISO 10791-7 o he s anda dised
componen [27]. This wo kpiece is speci ied o e i y he p oduc ion accu acy o h ee-axis
kinema ics wi h he op ion o assessing se e al dimensional and shape de ia ions. Publica ions [22]
and [28] desc ibe he e ec o machine load on he posi ion o he o a y axis, as well as he esul ing
o ien a ion e o s. When assessing he geome ic e o s o he machine, i is necessa y o conside he
machining o ces and hea dissipa ion in he machine.
This publica ion is ocused on desc ibing he dependence be ween he olume ic accu acy o
he machine and he esul ing wo king accu acy, assessed on he e o o wo kpiece oundness
unde inishing condi ions o machining. The dependence be ween olume ic accu acy and
oundness e o is desc ibed in publica ion [29], acco ding o ISO 230-4.
The p esen ed expe imen ocuses on he e i ica ion o he co ela ion be ween he olume ic
accu acy o machines and p oduc ion accu acy. In his case, geome ic accu acy is ep esen ed by
olume ic accu acy. The measu emen s o olume ic accu acy a e based on he indi ec me hod,
using he sel -guiding lase in e e ome e Lase TRACER. This me hod is desc ibed, o example, in
[3]. In o de o assess he in luence o olume ic accu acy on he esul ing wo king accu acy, i is
impo an o obse e cons an ambien condi ions due o he epea abili y o he p oduc ion o es
wo kpieces. The nega i e e ec o empe a u e on he change in olume ic accu acy is desc ibed in
[30]. P oduc ion accu acy is ep esen ed in a es wo kpiece designed o e i y oundness e o . This
is hen e i ied by he Taly ond 595S measu ing de ice. The oundness esul s o he wo kpiece a e
hen compa ed o hose ob ained wi h he ci cula in e pola ion es , acco ding o ISO 230-4. The
measu ing de ice used is he Ballba QC20-w.
2. Expe imen al Se up
2.1. The S a egy o he Expe imen
The expe imen se up is shown in Figu e 1. The expe imen was di ided in o wo pa s. In he
i s pa , a h ee-axis machine ool was measu ed wi h i s basic se up, i.e., wi hou so wa e
compensa ion o he geome ic e o s o he machine. In he second se up, olume ic accu acy was
compensa ed o ; no o he geome ic e o compensa ions we e used. I is necessa y o moni o he
su ounding en i onmen h oughou he measu emen p ocess. Moni o ing was ca ied ou
acco ding o he p ocedu e desc ibed in [20].
Figu e 1. Expe imen se up.
In bo h pa s o he expe imen , ci cula in e pola ion measu emen s we e pe o med wi h he
Ballba QC20-w, RENISHAW (DBB) o machining wi hou DBB1 compensa ions and o machining
wi h DBB2 olume ic compensa ions, acco ding o ISO 230-4 [31]. Volume ic accu acy was
measu ed wi h he Lase TRACER, ETALON (LTc) wi hou LTc1 (Figu e 1–pa o he calib a ion)
compensa ions and wi h LTc2 (Figu e 1—pa o he ce i ica ion) olume ic compensa ions
ac i a ed. The nex s ep was he machining o he es wo kpiece (WP) wi hou so wa e WP1
geome ic compensa ions and wi h WP2 olume ic compensa ions ac i a ed. In he las s ep o each
cycle, an inspec ion o shape accu acy ( oundness) was pe o med using he Taly ond 595S om
Figu e 1. Expe imen se up.
In bo h pa s o he expe imen , ci cula in e pola ion measu emen s we e pe o med wi h he
Ballba QC20-w, RENISHAW (DBB) o machining wi hou DBB1 compensa ions and o machining
wi h DBB2 olume ic compensa ions, acco ding o ISO 230-4 [
31
]. Volume ic accu acy was measu ed
wi h he Lase TRACER, ETALON (LTc) wi hou LTc1 (Figu e 1—pa o he calib a ion) compensa ions
and wi h LTc2 (Figu e 1—pa o he ce i ica ion) olume ic compensa ions ac i a ed. The nex
s ep was he machining o he es wo kpiece (WP) wi hou so wa e WP1 geome ic compensa ions
Appl. Sci. 2020,10, 6233 4 o 18
and wi h WP2 olume ic compensa ions ac i a ed. In he las s ep o each cycle, an inspec ion
o shape accu acy ( oundness) was pe o med using he Taly ond 595S om Taylo Hobson (TH),
again o he wo kpiece wi hou ac i a ed so wa e TH1 compensa ions and wi h TH2 olume ic
compensa ions ac i a ed.
2.2. The CNC Machine Tool
The machining o es wo kpieces was ca ied ou on he h ee-axis e ical machine ools MCV
754QUICK and KOVOSVIT MAS and he SIEMENS Sinume ik 840D sl con ol sys em wi h he VCS
A3 op ion (a olume ic compensa ion sys em o h ee-axis machine ools).
Figu e 2is a schema ic diag am o he expe imen se up on a machine ool showing he wo kpiece
loca ion in he machine wo kspace, he posi ion o he measu ing de ices, he ange o ci cula
in e pola ion es and he compensa ed wo kspace o he machine.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 o 18
Taylo Hobson (TH), again o he wo kpiece wi hou ac i a ed so wa e TH1 compensa ions and
wi h TH2 olume ic compensa ions ac i a ed.
2.2. The CNC Machine Tool
The machining o es wo kpieces was ca ied ou on he h ee-axis e ical machine ools MCV
754QUICK and KOVOSVIT MAS and he SIEMENS Sinume ik 840D sl con ol sys em wi h he VCS
A3 op ion (a olume ic compensa ion sys em o h ee-axis machine ools).
Figu e 2 is a schema ic diag am o he expe imen se up on a machine ool showing he
wo kpiece loca ion in he machine wo kspace, he posi ion o he measu ing de ices, he ange o
ci cula in e pola ion es and he compensa ed wo kspace o he machine.
(a) (b)
Figu e 2. Machining o he es wo kpiece. (a) Posi ion o he wo kpiece in he machine; (b)
wo kpiece machining.
The wo kspace o he machine and he measu ed space a e de ined in Table 1:
Table 1. Measu emen ange o he MCV 754QUICK machine ool.
Axis S a Axis WS/S a Measu e MS [mm] End Axis WS/End Measu e MS [mm] Leng h
[mm]
X 0/100 754/550 450
Y 0/0 500/500 500
Z −550/−400 0/0 400
2.3. The Wo kpiece
The shape and dimensions o he wo kpiece we e chosen o be as consis en as possible wi h he
pa ame e s o he es , acco ding o ISO 230-4, o he ci cula in e pola ion o wo linea axes. Th ee
diame e s, 100, 200 and 300 mm, a e inspec ed on he wo kpiece.
The machining echnology, wo kpiece ma e ial, machining posi ion and clamping me hod a e
iden ical o bo h pa s. The dimensions o he wo kpiece and i s shape a e machining a e shown in
Figu e 3. The machining pa ame e s a e desc ibed in Table 2.
Figu e 2.
Machining o he es wo kpiece. (
a
) Posi ion o he wo kpiece in he machine; (
b
)
wo kpiece machining.
The wo kspace o he machine and he measu ed space a e de ined in Table 1:
Table 1. Measu emen ange o he MCV 754QUICK machine ool.
Axis S a Axis WS/S a
Measu e MS [mm]
End Axis WS/End
Measu e MS [mm] Leng h [mm]
X 0/100 754/550 450
Y 0/0 500/500 500
Z−550/−400 0/0 400
2.3. The Wo kpiece
The shape and dimensions o he wo kpiece we e chosen o be as consis en as possible wi h he
pa ame e s o he es , acco ding o ISO 230-4, o he ci cula in e pola ion o wo linea axes. Th ee
diame e s, 100, 200 and 300 mm, a e inspec ed on he wo kpiece.
Appl. Sci. 2020,10, 6233 5 o 18
The machining echnology, wo kpiece ma e ial, machining posi ion and clamping me hod a e
iden ical o bo h pa s. The dimensions o he wo kpiece and i s shape a e machining a e shown in
Figu e 3. The machining pa ame e s a e desc ibed in Table 2.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 o 18
(a) (b)
Figu e 3. (a) Wo kpiece diag am and (b) ep esen a ion.
Table 2. Cu ing es pa ame e s.
Cu ing Pa ame e
Speed 200 m/min
Feed 0.1 mm/ oo h
Dep h 0.02 mm
Wid h 50 mm
Cu ing Tool Spec.
Ma e ial Solid ca bon
Type Endmill
No. o lu es 4
Diame e 16 mm
Holde ISO40 ER25
Ma e ial Spec. Ma e ial EN AW-2007
Dimension ϕ300–150 mm
2.4. Measu emen Se ing
The ollowing subsec ions p o ide basic in o ma ion abou he measu ing de ice used in he
expe imen .
2.4.1. Ci cula i y Tes s
Two ci cula i y es s we e pe o med based on he p inciple o ci cula in e pola ion, acco ding
o ISO 230-4. The i s one o he calib a ion cycle e e ed o as DBB 1 and he o he o he
e i ica ion cycle e e ed o as DBB 2.
The eed a es we e chosen so ha dynamic e o s om he d i es o he machine could no
a ec he esul s o he ci cula i y e o s.
In publica ion [32], he e ec s o dynamic e o s in he wo kpiece a e p esen ed. Speci ically,
he e ec o he e e sal spikes on he Y-axis, which was app oxima ely 120 µm ou o a o al
ci cula i y e o o 143 µm, is desc ibed in de ail. In his case, o he e o s a e negligible wi h espec
o his e o .
Table 3 shows he echnical speci ica ions o he Ballba QC20-w.
Table 3. Ballba QC20-w speci ica ions [33].
I em Speci ica ion Uni s
Senso accu acy (a 20 °C) ±0.5 µm
Senso esolu ion 0.1 µm
Sys em accu acy ±1.25 µm
Measu ing unce ain y (k = 2) 0.7 + 0.003 × L µm
Maximum sampling a e 1000 Hz
Figu e 3. (a) Wo kpiece diag am and (b) ep esen a ion.
Table 2. Cu ing es pa ame e s.
Cu ing Pa ame e
Speed 200 m/min
Feed 0.1 mm/ oo h
Dep h 0.02 mm
Wid h 50 mm
Cu ing Tool Spec.
Ma e ial Solid ca bon
Type Endmill
No. o lu es 4
Diame e 16 mm
Holde ISO40 ER25
Ma e ial Spec. Ma e ial EN AW-2007
Dimension φ300–150 mm
2.4. Measu emen Se ing
The ollowing subsec ions p o ide basic in o ma ion abou he measu ing de ice used in
he expe imen .
2.4.1. Ci cula i y Tes s
Two ci cula i y es s we e pe o med based on he p inciple o ci cula in e pola ion, acco ding o
ISO 230-4. The i s one o he calib a ion cycle e e ed o as DBB 1 and he o he o he e i ica ion
cycle e e ed o as DBB 2.
The eed a es we e chosen so ha dynamic e o s om he d i es o he machine could no a ec
he esul s o he ci cula i y e o s.
In publica ion [
32
], he e ec s o dynamic e o s in he wo kpiece a e p esen ed. Speci ically, he
e ec o he e e sal spikes on he Y-axis, which was app oxima ely 120
µ
m ou o a o al ci cula i y
e o o 143
µ
m, is desc ibed in de ail. In his case, o he e o s a e negligible wi h espec o his e o .
Table 3shows he echnical speci ica ions o he Ballba QC20-w.

Appl. Sci. 2020,10, 6233 6 o 18
Table 3. Ballba QC20-w speci ica ions [33].
I em Speci ica ion Uni s
Senso accu acy (a 20 ◦C) ±0.5 µm
Senso esolu ion 0.1 µm
Sys em accu acy ±1.25 µm
Measu ing unce ain y (k =2) 0.7 +0.003 ×Lµm
Maximum sampling a e 1000 Hz
The measu emen was pe o med in he cen e o he expec ed machining o he wo kpiece a
a eed a e equal o he eed a e du ing machining, i.e., 400 mm/min. Based on he esul s o he
measu emen , he unce ain y alues o measu ing we e hen de e mined o indi idual diame e s.
When en e ed in o he ela ionship o calcula ion o measu ing unce ain y o 300 mm diame e
DBB1, measu ing unce ain y was 0.8 µm, and o DBB2, i was 0.7 µm.
2.4.2. Volume ic Accu acy
The olume ic accu acy o he machine was e i ied o he calib a ion cycle (LTc1) and he
e i ica ion cycle (LTc2) acco ding o he p ocedu e desc ibed in [
5
]. In e media e igid body ype 3
(IRB3) was chosen as a kinema ic model. Du ing he measu emen , 1112 poin s in measu ed space
a e measu ed, including e e sal measu emen . The eed a e o he machine axes was chosen o
be 6000 mm/min in o de o minimise measu emen ime. F om he calib a ion measu emen , a
compensa ion ile ( olume ic compensa ion sys ems (VCS), Siemens) was also ob ained and ac i a ed
in he machine ool.
Table 4shows he echnical speci ica ions o he measu ing de ice Lase TRACER.
Table 4. Lase TRACER speci ica ions.
I em Speci ica ion Uni s
Resolu ion 0.001 µm
Measu ing unce ain y (k =2) 0.2 +0.3 ×Lµm
Measu ing ange 0.2–18 m
Ambien condi ions we e moni o ed du ing calib a ion and he e i ica ion measu emen s. These
a e lis ed in Tables 5and 6. In he calib a ion measu emen s, empe a u e change on he X-axis did
no exceed 0.3
◦
C, 0.2
◦
C on he Y-axis and 0.6
◦
C on he Z-axis. These condi ions can be conside ed
s able o calib a ion measu emen s LTc1 (see Sec ion 3.1). The p inciple o measu ing and de e mining
Lase TRACER posi ions (P1, P2, P3 and P4) is desc ibed in publica ions [4,5].
Table 5. Condi ions o calib a ion measu emen .
Posi ion o
Measu emen
Time o
Measu emen
[Min]
X-Axis
Tempe a u e [◦C]
Y-Axis
Tempe a u e [◦C]
Z-Axis
Tempe a u e [◦C]
P1 16 19.8 19.5 20.6
P2 13 19.7 19.5 20.4
P3 9 19.7 19.5 20.3
P4 12 19.6 19.4 20.1
Appl. Sci. 2020,10, 6233 7 o 18
Table 6. Condi ions o e i ica ion measu emen .
Posi ion o
Measu emen
Time o
Measu emen
[Min]
X-Axis
Tempe a u e [◦C]
Y-Axis
Tempe a u e [◦C]
Z-Axis
Tempe a u e [◦C]
P1 12 20.9 20.2 22.3
P2 11 21.0 20.3 22.4
P3 8 21.0 20.4 22.6
P4 11 21.1 20.7 21.6
In he e i ica ion measu emen s, empe a u e change on he X-axis did no exceed 0.3
◦
C, 0.6
◦
C
on he Y-axis and 1.0
◦
C on he Z-axis. These condi ions can be de e mined as an e alua ion o he
e i ica ion measu emen LTc2 o he olume ic accu acy o he machine ool (see Sec ion 3.1).
2.4.3. Roundness Measu emen
Ve i ica ion o p oduc ion accu acy was pe o med on he Taylo Hobson Taly ond 595S oundness
measu ing ins umen (Figu e 4), which can be ound in he labo a o ies o he Czech Me ology
Ins i u e (CMI). The echnical speci ica ions o he ins umen a e gi en in Table 7.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 o 18
2.4.3. Roundness Measu emen
Ve i ica ion o p oduc ion accu acy was pe o med on he Taylo Hobson Taly ond 595S
oundness measu ing ins umen (Figu e 4), which can be ound in he labo a o ies o he Czech
Me ology Ins i u e (CMI). The echnical speci ica ions o he ins umen a e gi en in Table 7.
Figu e 4. Taly ond 595S, wo kpiece measu emen .
Table 7. Taly ond 595S speci ica ions [32].
I em Speci ica ion Uni s
Maximum componen diame e 400 mm
Maximum componen weigh 40 kg
Radial limi o e o
L [mm] +/− (0.0075 + 0.0002 × L) µm
Axial limi o e o
R [mm] +/− (0.0015 + 0.0002 × R) µm
Expanded unce ain y (k = 2) o a senso ange o 0.4 mm U0.4 0.063 µm
3. Expe imen Resul s
This sec ion desc ibes he esul s ob ained by measu ing he olume ic and geome ic accu acy
o he CNC machine ool and he oundness e o o he wo kpieces. We can desc ibe up o 21
geome ic e o s o he h ee-axis machine ool— he geome ic e o desc ip ion is shown in Figu e
5. The expe imen was ca ied ou acco ding o he p ocedu e shown in Figu e 1.
Figu e 5. Geome ic e o s o he h ee-axis e ical machining cen e [5].
Figu e 4. Taly ond 595S, wo kpiece measu emen .
Table 7. Taly ond 595S speci ica ions [32].
I em Speci ica ion Uni s
Maximum componen diame e 400 mm
Maximum componen weigh 40 kg
Radial limi o e o
L [mm] +/−(0.0075 +0.0002 ×L) µm
Axial limi o e o
R [mm] +/−(0.0015 +0.0002 ×R) µm
Expanded unce ain y (k =2) o a senso ange o 0.4 mm U0.4 0.063 µm
3. Expe imen Resul s
This sec ion desc ibes he esul s ob ained by measu ing he olume ic and geome ic accu acy
o he CNC machine ool and he oundness e o o he wo kpieces. We can desc ibe up o 21
geome ic e o s o he h ee-axis machine ool— he geome ic e o desc ip ion is shown in Figu e 5.
The expe imen was ca ied ou acco ding o he p ocedu e shown in Figu e 1.
Appl. Sci. 2020,10, 6233 8 o 18
Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 o 18
2.4.3. Roundness Measu emen
Ve i ica ion o p oduc ion accu acy was pe o med on he Taylo Hobson Taly ond 595S
oundness measu ing ins umen (Figu e 4), which can be ound in he labo a o ies o he Czech
Me ology Ins i u e (CMI). The echnical speci ica ions o he ins umen a e gi en in Table 7.
Figu e 4. Taly ond 595S, wo kpiece measu emen .
Table 7. Taly ond 595S speci ica ions [32].
I em Speci ica ion Uni s
Maximum componen diame e 400 mm
Maximum componen weigh 40 kg
Radial limi o e o
L [mm] +/− (0.0075 + 0.0002 × L) µm
Axial limi o e o
R [mm] +/− (0.0015 + 0.0002 × R) µm
Expanded unce ain y (k = 2) o a senso ange o 0.4 mm U0.4 0.063 µm
3. Expe imen Resul s
This sec ion desc ibes he esul s ob ained by measu ing he olume ic and geome ic accu acy
o he CNC machine ool and he oundness e o o he wo kpieces. We can desc ibe up o 21
geome ic e o s o he h ee-axis machine ool— he geome ic e o desc ip ion is shown in Figu e
5. The expe imen was ca ied ou acco ding o he p ocedu e shown in Figu e 1.
Figu e 5. Geome ic e o s o he h ee-axis e ical machining cen e [5].
Figu e 5. Geome ic e o s o he h ee-axis e ical machining cen e [5].
3.1. Volume ic Accu acy o he Machine Tool
The olume ic accu acy o he machine is e alua ed o LTc1 calib a ion and LTc2 e i ica ion.
Wi hin he amewo k o he pe o med expe imen , geome ic e o s and olume ic e o s (
e
)
we e ound. Figu e 6shows he e o s o bo h he calib a ion and e i ica ion measu emen s o he
machine wo kspace ob ained wi h he Lase TRACER. These e o s a e desc ibed acco ding o ISO
230-1 con en ions.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 o 18
3.1. Volume ic Accu acy o he Machine Tool
The olume ic accu acy o he machine is e alua ed o LTc1 calib a ion and LTc2 e i ica ion.
Wi hin he amewo k o he pe o med expe imen , geome ic e o s and olume ic e o s ( e)
we e ound. Figu e 6 shows he e o s o bo h he calib a ion and e i ica ion measu emen s o he
machine wo kspace ob ained wi h he Lase TRACER. These e o s a e desc ibed acco ding o ISO
230-1 con en ions.
Figu e 6. Geome ic e o s calcula ed wi h he help o olume ic accu acy measu emen s.
Figu e 7 is a g aphical ep esen a ion o olume ic e o dis ibu ion in he machine
wo kspace. The esul s show ha olume ic e o ( e) dec eased signi ican ly, om 49 µm o 14 µm.
Fu he mo e, he posi ioning e o s on he EXX, EYY and EZZ axes we e educed and he squa eness
e o s o ela i e axes EC0Y, EB0Z and EA0Z we e signi ican ly educed. These e o s we e also educed
in he esul s ob ained om he ci cula in e pola ion es , acco ding o ISO 230-4 (see Sec ion 3.2).
(a) (b)
Figu e 6. Geome ic e o s calcula ed wi h he help o olume ic accu acy measu emen s.
Figu e 7is a g aphical ep esen a ion o olume ic e o dis ibu ion in he machine wo kspace.
The esul s show ha olume ic e o (
e
) dec eased signi ican ly, om 49
µ
m o 14
µ
m. Fu he mo e,
he posi ioning e o s on he E
XX
, E
YY
and E
ZZ
axes we e educed and he squa eness e o s o ela i e
axes E
C0Y
, E
B0Z
and E
A0Z
we e signi ican ly educed. These e o s we e also educed in he esul s
ob ained om he ci cula in e pola ion es , acco ding o ISO 230-4 (see Sec ion 3.2).
Appl. Sci. 2020,10, 6233 9 o 18
Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 o 18
3.1. Volume ic Accu acy o he Machine Tool
The olume ic accu acy o he machine is e alua ed o LTc1 calib a ion and LTc2 e i ica ion.
Wi hin he amewo k o he pe o med expe imen , geome ic e o s and olume ic e o s ( e)
we e ound. Figu e 6 shows he e o s o bo h he calib a ion and e i ica ion measu emen s o he
machine wo kspace ob ained wi h he Lase TRACER. These e o s a e desc ibed acco ding o ISO
230-1 con en ions.
Figu e 6. Geome ic e o s calcula ed wi h he help o olume ic accu acy measu emen s.
Figu e 7 is a g aphical ep esen a ion o olume ic e o dis ibu ion in he machine
wo kspace. The esul s show ha olume ic e o ( e) dec eased signi ican ly, om 49 µm o 14 µm.
Fu he mo e, he posi ioning e o s on he EXX, EYY and EZZ axes we e educed and he squa eness
e o s o ela i e axes EC0Y, EB0Z and EA0Z we e signi ican ly educed. These e o s we e also educed
in he esul s ob ained om he ci cula in e pola ion es , acco ding o ISO 230-4 (see Sec ion 3.2).
(a) (b)
Figu e 7.
G aphical ep esen a ion o he olume ic e o s in he machine wo kspace: (
a
) wi hou
olume ic compensa ion o 49
µ
m—calib a ion; (
b
) wi h olume ic compensa ion o 14
µ
m— e i ica ion.
3.2. Geome ic Accu acy
The geome ic accu acy o he machine ool was de e mined by he ci cula in e pola ion es ,
acco ding o ISO 230-4. The e alua ion o indi idual machine e o s was ca ied ou using he so wa e
p o ided wi h he Ballba QC20-w.
In he pe o med es , geome ic accu acy was always e alua ed wi hou DBB1 olume ic
compensa ion bu wi h DBB2 olume ic compensa ion.
Figu e 8shows he esul s o he ci cula in e pola ion measu emen s in he XY-plane wi h a
diame e o 300 mm and a eed a e o 400 mm/min, and Table 8shows he selec ed pa ame e s o he
ci cula i y es o DBB1 and DBB2.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 o 18
Figu e 7. G aphical ep esen a ion o he olume ic e o s in he machine wo kspace: (a) wi hou
olume ic compensa ion o 49 µm—calib a ion; (b) wi h olume ic compensa ion o 14
µm— e i ica ion.
3.2. Geome ic Accu acy
The geome ic accu acy o he machine ool was de e mined by he ci cula in e pola ion es ,
acco ding o ISO 230-4. The e alua ion o indi idual machine e o s was ca ied ou using he
so wa e p o ided wi h he Ballba QC20-w.
In he pe o med es , geome ic accu acy was always e alua ed wi hou DBB1 olume ic
compensa ion bu wi h DBB2 olume ic compensa ion.
Figu e 8 shows he esul s o he ci cula in e pola ion measu emen s in he XY-plane wi h a
diame e o 300 mm and a eed a e o 400 mm/min, and Table 8 shows he selec ed pa ame e s o he
ci cula i y es o DBB1 and DBB2.
(a) (b)
Figu e 8. Ci cula i y es —300 mm diame e : (a) wi hou olume ic compensa ion; (b) wi h
olume ic compensa ion.
Table 8. Resul s o he ci cula i y es —300 mm diame e .
XY–300 Ci cula i y
[µm]
Squa eness
[µm/m]
Scaling
Misma ch [µm]
Posi ional
Tole ance [µm]
Unce ain y (k =
2) [µm]
DBB1 10.5 22.4 12.3 27.6 0.8
DBB2 4.5 −6.2 −4.0 8.4 0.7
Figu e 9 shows he esul s o he ci cula in e pola ion measu emen s in he XY-plane wi h a
diame e o 200 mm and a eed a e o 400 mm/min. Table 9 shows he indi idual es pa ame e s.
Figu e 8.
Ci cula i y es —300 mm diame e : (
a
) wi hou olume ic compensa ion; (
b
) wi h
olume ic compensa ion.
Table 8. Resul s o he ci cula i y es —300 mm diame e .
XY–300 Ci cula i y
[µm]
Squa eness
[µm/m]
Scaling
Misma ch
[µm]
Posi ional
Tole ance [µm]
Unce ain y
(k =2) [µm]
DBB1 10.5 22.4 12.3 27.6 0.8
DBB2 4.5 −6.2 −4.0 8.4 0.7
Appl. Sci. 2020,10, 6233 16 o 18
The acqui ed knowledge abou he beha iou o machine ools in e ms o geome ic accu acy can
be u he used o p edic he dimensional and shape e o s o wo kpieces. The esul s a e applicable
o inishing echnologies whe e machining o ces a e negligible and do no bu den he machine wi h
de o ma ion om s a ic compliance.
5. Conclusions
This pape desc ibes a new, complex app oach o e i ying he dependence be ween he geome ic,
olume ic and wo king accu acy o CNC machine ools. The conclusions o his wo k se e u he
esea ch in he dimensional and o m de ia ion p edic ion o wo kpieces. The expe imen p o es ha
he esolu ion o he me hod co esponds o he equi emen s o p ecise p oduc ion, whe e de ia ions
a e in he dimension ange om 5 o 10 µm.
An imp o emen in he olume ic accu acy o a small h ee-axis machine ool by 70% esul s in
an up o 58% imp o emen in ci cula i y in an unloaded s a e, measu ed acco ding o ISO 230-4, and a
40% imp o emen in he RON o he wo kpiece unde inishing condi ions o machining.
I is also e iden om he esul s o he expe imen ha ci cula i y e o is signi ican ly a ec ed
by he squa eness e o o wo ela i e axes in he machining plane, bo h in he ci cula in e pola ion
es o wo linea axes acco ding o ISO 230-4 and he impac on he wo kpiece RON .
In a small CNC machine ool, including MCV754QUICK, a 40% imp o emen in RON can be
achie ed h ough he ac i a ion o olume ic compensa ion. He e, he ne measu emen ime was
50 min. The ime i ook o posi ion he Lase TRACER, implemen he compensa ions and e i y
using he Ballba QC20-w was app oxima ely 125 min. This is a highly e ec i e way o inc easing
p oduc ion accu acy in e ms o machine measu emen ime, implemen a ion o compensa ion ables
and e i ica ion.
Fu he esea ch in his a ea will be ocused on he e i ica ion o dimensional accu acy unde
a ious machining condi ions.
These esul s ha e he po en ial o u he s eamline compensa ions, leading o an inc ease in
p oduc ion accu acy, and can be used o p edic he geome ic, olume ic and p oduc ion accu acy o
machine ools, based on he p inciple desc ibed, o example, in [34,35].
Au ho Con ibu ions:
Concep ualisa ion, M.H.; me hodology, M.H.; o mal analysis, M.H. and R.J.; in es iga ion,
M.H., J.V. and J.S. (Jan S amek), esou ces, M.H. and R.J.; da a cu a ion, M.H. and R.J.; w i ing—o iginal d a
p epa a ion, M.H.; w i ing— e iew and edi ing, R.J.; isualisa ion, M.H. and R.J.; supe ision, P.B., J.S. (Jan
Smolik) and P.H.; p ojec adminis a ion, M.H.; unding acquisi ion, P.B. and J.S. (Jan Smolik). All au ho s ha e
ead and ag eed o he published e sion o he manusc ip .
Funding:
This esea ch was unded by Czech Minis y o Educa ion, You h and Spo s, g an numbe
CZ.02.1.01/0.0/0.0/16_026/0008404—Manu ac u ing enginee ing and P ecision Enginee ing.
Acknowledgmen s:
The au ho s would like o acknowledge unding suppo om he Czech Minis y o
Educa ion, You h and Spo s unde he p ojec CZ.02.1.01/0.0/0.0/16_026/0008404 “ Manu ac u ing enginee ing and
P ecision Enginee ing” inanced by he OP RDE (ERDF). The p ojec is also co- inanced by he Eu opean Union.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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