Experimental Study of the Volumetric Error Effect on the Resulting Working Accuracy—Roundness

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 This pape p esen s new and unpublished ela ions be ween he olume ic accu acy o he machine ool and he RON o he wo kpiece.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 . Re e ences 1. Ramesh, R.; Mannan, M.; Poo, A. E o compensa ion in machine ools—A e iew: Geome ic, cu ing- o ce induced and ix u e-dependen e o s. In . J. Mach. Tools Manu . 2000,40, 1235–1256. [C ossRe ] 2. Iba aki, S.; Sawada, M.; Ma suba a, A.; Ma sushi a, T. Machining es s o iden i y kinema ic e o s on i e-axis machine ools. P ecis. Eng. 2010,34, 387–398. [C ossRe ] 3. 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