Laboratory machine verification of force transmission provided by friction acting on the drive drum of a conveyor belt

Ci a ion: H abo ský, L.; Neniˇcka, P.; F ies, J. Labo a o y Machine Ve i ica ion o Fo ce T ansmission P o ided by F ic ion Ac ing on he D i e D um o a Con eyo Bel . Machines 2023,11, 544. h ps:// doi.o g/10.3390/machines11050544 Academic Edi o : Sheng Li Recei ed: 24 Ap il 2023 Re ised: 9 May 2023 Accep ed: 9 May 2023 Published: 11 May 2023 Copy igh : © 2023 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/). machines A icle Labo a o y Machine Ve i ica ion o Fo ce T ansmission P o ided by F ic ion Ac ing on he D i e D um o a Con eyo Bel Leopold H abo ský* , Pe Neniˇcka and Jiˇ íF ies Depa men o Machine and Indus ial Design, Facul y o Mechanical Enginee ing, VSB-Technical Uni e si y o Os a a, 70800 Os a a, Czech Republic; pe [email p o ec ed] (P.N.); [email p o ec ed] (J.F.) *Co espondence: [email p o ec ed] Abs ac : The pape p esen s he measu ed alues o ensile o ces ac ing on ansmission idle s in he uppe and lowe un o a con eyo bel placed on a labo a o y machine designed a he Depa men o Machine and Indus ial Design, Facul y o Mechanical Enginee ing, VSB-Technical Uni e si y o Os a a. The ensile o ces de ec ed by wo s ain gauge load cells and eco ded using DEWESo so wa e we e used o calcula e he ic ion coe icien , which ac s on he su ace o he d i ing d um casing and he con eyo bel . The ic ion coe icien a he slip poin , o du ing he slippage o he con eyo bel on he ubbe o s eel casing o he d i ing d um, was de e mined o wo s a es o he su aces ha a e in con ac . Expe imen al measu emen s on a labo a o y machine de e mined ou alues o ic ion coe icien s o wo ypes o d um su aces and o wo s a es o con ac su aces, which we e compa ed wi h he ecommended s anda d alues. The measu ed alues eached highe alues in compa ison wi h he alues gi en by he CSN s anda ds. The highes de ia ion o 273.3% is achie ed using a s eel we su ace, and he lowes de ia ion o 106.3% is achie ed when using a ubbe d y lining o he d i ing d um casing. On he p esen ed labo a o y machine, i is possible o measu e ensile o ces o di e en speeds o mo emen , di e en bel angles on he d i ing d um, a ious ypes o bel su aces, di e en ypes o d um casing linings, and di e en sizes o ension o ces o he endless loop o he con eyo bel . Fo hese cha ac e is ics o he con eyo bel , he magni ude o he ic ion coe icien ac ing be ween he bel and he d um su aces can be de e mined. Keywo ds: labo a o y machine; con eyo bel ; coe icien o ic ion; d i e d um; d um coa ing; ensile o ces exe ed on he bel 1. In oduc ion The bel o he bel con eyo is d i en by ic ional o ces ha a e ansmi ed be ween he su ace o he d i ing d um casing/shell and he con eyo bel . Thus, he o al mo e- men esis ance o he con eyo bel is o e come by he d i ing o ces gene a ed by he bel con eyo d i e placed on he d i ing d ums. In a pape [ 1 ], An oniak p esen s he heo e ical basis used o build a new gene a ion o bel con eyo s. These con eyo s a e cha ac e ized by he be e ene gy-sa ing pa ame e s o hei un anspo and hei highe eliabili y. The solu ion o o ce ela ionships o he d i ing d ums is based on Eule (-Ey elwein) Equa ion (1). The Eule –Ey elwein o mula, w i en by Leonha d Eule (1707–1783) and Johann Al- be Ey elwein (1764–1848), desc ibes he ic ion o a la bel su ounding a cylind ical d um [2]. Konyukho e al. s a e in [ 3 ] ha he solu ion o he gene alized Eule –Ey elwein, o he bel ic ion issue, is a s and-alone ask ecen ly o mula ed o a ope placed in a sliding equilib ium on an a bi a y su ace. I b ings a new se o benchma k issues o Machines 2023,11, 544. h ps://doi.o g/10.3390/machines11050544 h ps://www.mdpi.com/jou nal/machines Machines 2023,11, 544 2 o 19 he e i ica ion o a ope/beam placed on a su ace/solid con ac and i s algo i hms. No only a pulling o ce a io bu also he posi ion o he cu e on an a bi a y igid su ace, wi hs anding he mo ion in he d agging di ec ion, should be e i ied. Ha ada and Hi osa o, in a icle [ 4 ], use an endless ope (loop- ope), u ning a ound an endless pulley and an endless winch. As ic ion o ces be ween he cable and he d um ans e he cable ension, he slipping o he cable, which is domina ed by he well-known Eule –Ey elwein o mula, is aking in o conside a ion he s a ics o he E-CDPR. In his pape , a new in e p e a ion o he Eule –Ey elwein’s o mula is p oposed by using a g aph in which he non-slipping condi ion is exp essed as an a ea in he cable ension. Konyukho e al., in a icles [ 5 – 7 ], s a e ha wi hin he ini e elemen implemen a ion, he isogeome ic app oach is used o model cu ilinea cables, and he igid su aces can be de ined in gene al ia NURB su ace splines. Ve i ica ion o he ini e elemen algo i hm is gi en using he well-known analy ical solu ion o he Eule –Ey elwein ask—a ope placed on a cylind ical su ace. Bulín and Hajžman, in hei a icle [ 8 ], p esen a bel -cylinde in e ac ion model based on he absolu e nodal coo dina e o mula ion o beam- ini e elemen s, which ake in o conside a ion he nonlinea con ac o ces ac ing be ween a beam and a igid cylinde . Ma e al. in pape [ 9 ] p esen an exclusi e es ing ig ha was buil o expe imen ally in es iga e ic ion and slip a he ele a o ac ion in e ace, p o ided unde a ious ac ion condi ions. Shi-zai and Meng-gang, in he a icle [ 10 ], p esen he go e ning equa ions de eloped by hem, which a e based on ca ena y heo y and he Eule –Ey elwein’s equa ion. The go - e ning equa ions o he h ee-dimensional sliding cable elemen s, wi h a known uns essed cable leng h and wi h known ensile o ces, a e espec i ely de eloped, accoun ing o he he mal e ec and sliding ic ion. Gładysiewicz e al., in a icle [ 11 ], p esen he p ima y pa ame e de e mining he alue o he esis ance o mo ion o he bel con eyo , which is he main esis ance coe icien , and is also e e ed o as he a i icial o ic i e ic ion coe icien . This coe icien is p ima ily used o calcula ing bel con eyo esis ance o mo ion acco dingly o DIN 22101, PN-93/M-46552, and ISO 5048 s anda ds. Munzenbe ge and Wheele speci y in a icle [ 12 ] ha he inden a ion olling esis ance o con eyo bel s is an impo an design conside a ion o long bel con eyo s and can also be impo an o hea ily loaded bel con eyo s. Inden a ion olling esis ance is dependen on he p ope ies o he con eyo bel , including he ca cass and bo om co e as well as p ope ies o he con eyo bel , including induced loads, he bel speed, ambien empe a u e, and he idle oll diame e . Fedo ko e al. desc ibe in a icle [ 13 ] he achie ed esea ch esul s ega ding he p ope ies o smoo h con eyo bel s de e mined h ough a ensile loading es o examine he beha io o he inne s uc u e o he bel samples. They p esen ha when he bel is subjec ed o long- e m s ain, he bel elaxa ion e ec is obse ed, and changes may occu o he inne s uc u e o he bel . The ensile es a a cons an eloci y de e mines he load s eng h limi o he s ip samples. K ól e al., in a icle [ 14 ], desc ibe a me hod o measu ing mo emen esis ances o mo ion o a single h ee- olle idle se wi h he use o a specially designed measu ing s and. The s and allows conduc ing measu emen s in eal ope a ing condi ions and wi h a a iable s eam o bulk ma e ial. In a icle [ 15 ], au ho s Rudolphi and Reicks desc ibe he one-dimensional Winkle ounda ion and a gene alized iscoelas ic Maxwell solid model o he bel backing ma e ial used o de e mine he esis ance o mo ion o a con eyo bel o e idle s. The iscoelas ic ma e ial model is a gene aliza ion o he h ee-pa ame e Maxwell model ha has p e i- ously been used o p edic he e ec i e ic ional coe icien o he olling mo ion. The e alua ed measu ed da a, see a icle [ 16 ], we e used o ob ain unc ional ela ionships o he comp essibili y moduli o he bila e al Winkle elas ic ounda ion. Machines 2023,11, 544 3 o 19 H abo skýe al., in a icle [ 17 ], epo ha one o he possible ways o ans e he ac i e powe o a d i e uni o he ac ion elemen is o use ibe ic ion. When a s eel ope is used as he ac ion elemen , he e is a ans e o ac i e powe in he g oo e c ea ed on he pe ime e o he im o he d i ing ope shea e. The ansmission capabili y o he d i e is di ec ly p opo ional o he size o he angle o he w ap and he shea ic ion coe icien o he ope su ace when he ope is in con ac wi h he su ace o he g oo e wall. The pape [ 18 ] by K ól e al. p esen s he esul o esea ch and analyses ca ied ou on he bel con eyo idle s’ o a ional esis ance, which is one o he key ac o s indica ing he quali y o he idle s. The o a ional esis ance o he ension olle s is an impo an ac o in he o al esis ance o mo ion o he bel con eyo . In a icle [ 19 ], H abo skýe al. p esen ed ha due o he su icien con ac p essu e be ween he pulley g oo e and he su ace o he s eel cable, he s eel cable mo es as a esul o ibe ic ion. In gene al, i is possible o de ine ibe (also called bel ) ic ion as he esis ance ha is imposed on a lexible s eel cable sliding o e he ounded su ace o a pulley. The ic ional ansmission o he ac i e o ce is conside ed sa e i he e is no slippage o he cable in he pulley g oo e. In he e en o insu icien cable p essu e agains he pulley g oo e o insu icien ic ion, he anspo p ocess ails, and he li ing de ice is unable o pe o m i s unc ion. The heo e ical ela ionship o powe ansmission p o ided by ic ion ac ing om he d i e o he pulling elemen , in he case o using he en i e geome ic w ap angle α [ ad] o he con eyo bel on he d i ing d um, is displayed in (1) [ 20 ]. In his o mula, µ [-] is he ic ion coe icien be ween he bel and he d um, T 1 [N] is he ensile o ce in he bel un app oaching he d i ing d um, and T 2 [N] is he ensile o ce in he bel un lea ing he d i ing d um. T1 T2=eµ·α[N]⇒µ=1 α·lnT1 T2[-], (1) Rela ionship (1) de ines he equilib ium a he momen o impending ela i e mo e- men , i.e., o he condi ion in which he con eyo bel begins o slip on he su ace o he casing o lining o he d i ing d um. Bel slip, i.e., he ela i e mo emen be ween he bel and d um o e he en i e geome ic angle o he bel , occu s in he case o (2) [21]. I he pulling elemen is a la V-bel [ 22 – 24 ] o a con eyo bel [ 25 , 26 ], hen he ic ion coe icien T [-] is exp essed by he alue o shea ic ion µ [-] ac ing be ween he su aces ha a e in mu ual con ac . T1 T2 >eµ·α[-], (2) Bel slip on a d um should no occu in p ac ice, as i causes excessi e bel wea and ene gy loss due o ic ion, and he bel i sel may be consequen ly damaged by de eloping hea [ 27 ]. Slippages o con eyo bel s ha occu in bel con eyo s a e also he cause o many o he accompanying nega i e phenomena, e.g., high dynamic s ess o he con eyo bel s, hei join s, and all o he mechanical elemen s. In case o comple e slippage, hey lead o he collapse o he e u n un s a ions and a high o e load o he d i es. They dis up he hy hm o he con eyo line s a and p olong i s s a -up ime. They may cause bel ib a ions which lead o alling ma e ial, pollu ing he a eas o he con eyo s, e c. [ 28 ]. The d i e is he e o e designed so ha while main aining a ce ain slip sa e y on he d i ing d um, he ollowing ela ionship is applied (3). T1 T2 <eµ·α[-], (3) Machines 2023,11, 544 4 o 19 The ansmission o o ces, wi h he same o only sligh ly a iable ic ion coe icien be ween he bel and he d um µ [-], does no in ol e he en i e geome ical w ap angle α[deg] bu only a pa o i , he so-called employed w ap angle β[deg]. The maximum magni ude o he ansmi ed ci cum e en ial o ce on he d i ing d um is p opo ional o he size o he geome ic w ap angle α [deg], he ensile o ce in he lea ing bel un T 2 [N], and coe icien s o ic ion be ween he bel and d um µ [-]. As he alues α [deg] and T 2 [N] canno be chosen as unlimi ed alues o a bel con eyo , i is impo an o know and co ec ly de e mine he size µ [-], which, among o he hings, is o g ea impo ance when deciding on he use o mul i-d um d i es [29–31]. The ic ion coe icien µ [-] occu ing be ween he d i ing elemen (i.e., a con eyo bel o s eel ope) and he d i ing d um o ic ion disc canno be measu ed di ec ly. Howe e , i can be calcula ed om he ensile o ces in he con eyo bel o s eel ope and he ci cum e en ial o ce ac ing on he d i ing d um o ic ion disc [ 9 , 11 ], o α = β [deg] (i.e., a he slip limi ). The magni ude o he ic ion coe icien be ween he bel and he d um depends on he quali y o he d um and bel con ac su aces, he ype o ma e ial (lining) used o he d um su ace, and he s uc u al modi ica ions o he d um su ace (e.g., g oo ing, e c.). Based on he expe imen al measu emen s o he ic ion coe icien ob ained be ween he bel and he d um, i can be concluded ha wi h inc easing bel speed µ [-], i de- c eases. A speeds = 1.5 ÷ 2.0 m · s −1 . he dec ease is mo e p onounced han a highe speeds [ 21 ] (p.149). Values µ [-] dec ease wi h inc easing mean speci ic p essu e p [Pa] occu ing be ween he bel and he d um [27,31]. The measu ed alues i µ = µ (p) [-] aken o d y, we , and clay-co e ed d ums a e lis ed in [21] (p. 150). Values ecommended o he used w ap angle y o he ic ion coe icien µ [-], aken o he d y, we , and clay o soil-co e ed con ac su ace o he d i ing d um and he ubbe con eyo bel , as a unc ion o he d um lining (smoo h s eel, ubbe lining—a ow g oo es, polyu e hane lining—a ow g oo es and ce amic lining—a ow g oo es) a e gi en in [32] (p. 13). The ecommended alues o ic ion coe icien s µ [-] o con eyo bel s wi h ubbe o e lays and he ype o d um su ace design and o ope a ional s a es o con ac su aces a e also gi en in [33]. The wid h o he bel and he w ap angle do no a ec he alue o he ic ion coe icien µ[-] [28,30]. 2. Ma e ials and Me hods Figu e 1p esen s a 3Ddesign o alabo a o ymachine de eloped inSolidWo ks ® P emium 2012 SP5.0 so wa e by he Depa men o Machine and Indus ial Design, Facul y o Me- chanical Enginee ing, VSB-Technical Uni e si y o Os a a. Machines 2023, 11, x FOR PEER REVIEW 5 o 20 Figu e 1. 3D model o a labo a o y de ice de ec ing he ic ion coe icien in he con ac su ace o he con eyo bel and he d i ing d um lining. 1—d i ing d um, 2—idle φ 63 mm, 3—con eyo bel , 4, 7—idle holde , 5, 8—load cell, 6— e u n d um, 9—b ake mechanism, and 10—elec o-hy- d aulic de ice. By mo ing he axis o he con eyo idle 2 (Figu e 1) ho izon ally, i is possible o achie e a change in he w ap angle α [deg] o con eyo bel 3 on he ci cum e ence o he d i ing d um casing 1 o his labo a o y machine. The d i e d um 1, ma ked by i s p oduce as LAT216.1 [34] (wi h echnical pa ame- e s nb = 32 min−1, M2 = 441 N·m, and Fb = 4090 N), was pu chased om he company Blue ech L d. This d um wi h a diame e o Db = 216 mm is made o s eel and o a ed a a pe iphe al speed o b = 0.37 m·s−1 in bea ings p essed on a sha wi h a diame e o 40 mm. The d i e d um wi h i s buil -in plane a y gea box (a gea a io ip = 29.06) uses a h ee-phase elec ic mo o wi h he powe o Pe = 1.5 kW and nominal speed ne = 930·min−1. Con eyo bel 3 wi h he wid h B = 200 mm (does no a ec he alue o he ic ion coe icien µ [-] [28]). I is suppo ed in he uppe pa o he labo a o y machine by an idle , which is moun ed on a s eel s uc u e 4 ha can be e ically mo ed ela i e o he s eel ame o he machine. Con eyo bel wid h B = 0.2 m was selec ed conce ning he equi ed amoun o mean con ac p essu e p [Pa] (4) [33] ac ing be ween he con eyo bel and he d i ing d um [29]. ⋅ T + T 12 p = [Pa] DB b, (4) Fo he mean con ac p essu es p [Pa] in he ange om 0 ÷ 0.1 MPa o 0.7 ÷ 0.8 MPa, he e a e alues o ecommended ic ion coe icien s µ [-] o con eyo bel s wi h ubbe o e lays lis ed in [33] (p. 24). F om he ecommended alues, see [33] (p. 24), o coe i- cien s o ic ion µ [-], i is clea ha hei size dec eases ( o con eyo bel s wi h co on- based ex ile inse s, polyamide, and polyes e ) when he con ac p essu e p [Pa] [35] mag- ni ude inc eases. On he uppe beam o he s eel ame s uc u e in 4, a s ain gauge load cell 5 [36] is moun ed. The eye o he bol , which is sc ewed in o he in e nal h ead o he load cell senso 5, is pu on he hook o he hand chain hois 11, see Figu e 2. Figu e 1. 3D model o a labo a o y de ice de ec ing he ic ion coe icien in he con ac su - ace o he con eyo bel and he d i ing d um lining. 1—d i ing d um, 2—idle ϕ 63 mm, 3—con eyo bel , 4, 7—idle holde , 5, 8—load cell, 6— e u n d um, 9—b ake mechanism, and 10—elec o-hyd aulic de ice. Machines 2023,11, 544 5 o 19 By mo ing he axis o he con eyo idle 2 (Figu e 1) ho izon ally, i is possible o achie e a change in he w ap angle α [deg] o con eyo bel 3 on he ci cum e ence o he d i ing d um casing 1 o his labo a o y machine. The d i e d um 1, ma ked by i s p oduce as LAT216.1 [ 34 ] (wi h echnical pa ame e s n b = 32 min −1 , M 2 = 441 N · m, and F b = 4090 N), was pu chased om he company Blue ech L d. This d um wi h a diame e o D b = 216 mm is made o s eel and o a ed a a pe iphe al speed o b = 0.37 m · s −1 in bea ings p essed on a sha wi h a diame e o 40 mm. The d i e d um wi h i s buil -in plane a y gea box (a gea a io i p = 29.06) uses a h ee-phase elec ic mo o wi h he powe o Pe= 1.5 kW and nominal speed ne= 930·min−1. Con eyo bel 3 wi h he wid h B = 200 mm (does no a ec he alue o he ic ion coe icien µ [-] [ 28 ]). I is suppo ed in he uppe pa o he labo a o y machine by an idle , which is moun ed on a s eel s uc u e 4 ha can be e ically mo ed ela i e o he s eel ame o he machine. Con eyo bel wid h B = 0.2 m was selec ed conce ning he equi ed amoun o mean con ac p essu e p [Pa] (4) [ 33 ] ac ing be ween he con eyo bel and he d i ing d um [29]. p=T1+T2 Db·B[Pa], (4) Fo he mean con ac p essu es p [Pa] in he ange om 0 ÷ 0.1 MPa o 0.7 ÷0.8 MPa , he e a e alues o ecommended ic ion coe icien s µ [-] o con eyo bel s wi h ub- be o e lays lis ed in [ 33 ] (p. 24). F om he ecommended alues, see [ 33 ] (p. 24), o coe icien s o ic ion µ [-], i is clea ha hei size dec eases ( o con eyo bel s wi h co on-based ex ile inse s, polyamide, and polyes e ) when he con ac p essu e p [Pa] [ 35 ] magni ude inc eases. On he uppe beam o he s eel ame s uc u e in 4, a s ain gauge load cell 5 [ 36 ] is moun ed. The eye o he bol , which is sc ewed in o he in e nal h ead o he load cell senso 5, is pu on he hook o he hand chain hois 11, see Figu e 2. Machines 2023, 11, x FOR PEER REVIEW 6 o 20 Figu e 2. Chain hois suspended using h eaded ods on c oss-sec ion beams I and HEB (a) 3D model, (b) implemen ed design. 4—idle holde design, 5—load cell senso , and 11—hand chain hois . By sho ening he leng h o he chain ca ie o he chain hois 11, he e is a e ical shi o he idle holde 4 s uc u e occu ing, as a esul o which he angles γ [deg] and δ [deg] change on he con eyo bel 3 guided in he uppe un o he labo a o y machine. Con eyo bel 3 (guided a ound he e u n d um 6, see Figu e 1) is p essed du ing he expe imen al es s by a wooden lining ixed by bol s on he s eel s uc u e 9 o he su ace o he e u n d um casing 6. The s eel s uc u e 9 p essing o ce ac ing on he con- eyo bel 3, which, due o he magni ude o he p essing o ce, is also p essed agains he casing o he e u n d um 6, is caused by he elec o-hyd aulic appa a us o he EP se ies 10 [17,37]. Due o he ic ion o ce in con ac wi h he con eyo bel su ace and wooden lining, he speed o he con eyo bel dec eases. As he p essu e o ce o he wooden lining ac ing agains he con eyo bel inc eases, he ic ional “b aking” o ce also inc eases lin- ea ly, which causes a educ ion in he speed o he con eyo bel mo emen . A he mo- men when he ic ional o ce in he con ac su ace o he wooden lining and he con- eyo bel eaches he magni ude o he ac i e o ce on he ci cum e ence o he d i ing d um casing, he mo ing con eyo bel s ops (i.e., by i s b aking). The labo a o y machine is equipped wi h an elec o-hyd aulic de ice 10 [37] achie - ing a maximum a el heigh o 160 mm, a ac i e o ce o 1900 N, and an elec ic mo o wi h a powe consump ion o 450 W. Con eyo bel 3 in he lowe un is guided a ound he idle moun ed on he s eel s uc u e 7, which can slide e ically wi h mo emen el- a i e o he s eel ame o he labo a o y de ice. To he lowe beam o he s eel ame s uc u e, as in 7, a s ain gauge load cell 8 [36] is a ached. The inal labo a o y de ice, see Figu e 3 (o hese basic pa ame e s: heigh 1635 mm, leng h 2730 mm, wid h 780 mm, weigh app oxima ely 180 kg) equipped wi h load cells 5 and 8 enables he de ec ion and subsequen eco ding (using DEWESo X2 SP5 so wa e [38]) o ins an aneous alues o he ensile o ce ac ing in he uppe un (T1 [N]) and lowe (T2 [N]) un o he endless loops o he con eyo bel 3 in ime [s] o he p o ided meas- u emen . Using he known (ob ained by measu ing on his labo a o y machine) magni- udes o ensile o ces, we can calcula e, acco ding o he ela ionship (1), ic ion coe i- cien µ [-] a he slip poin (α = β [deg]) be ween he con eyo bel and he d i ing d um. Figu e 2. Chain hois suspended using h eaded ods on c oss-sec ion beams I and HEB ( a ) 3D model, (b) implemen ed design. 4—idle holde design, 5—load cell senso , and 11—hand chain hois . By sho ening he leng h o he chain ca ie o he chain hois 11, he e is a e ical shi o he idle holde 4 s uc u e occu ing, as a esul o which he angles γ [deg] and δ[deg] change on he con eyo bel 3 guided in he uppe un o he labo a o y machine. Con eyo bel 3 (guided a ound he e u n d um 6, see Figu e 1) is p essed du ing he expe imen al es s by a wooden lining ixed by bol s on he s eel s uc u e 9 o he su ace o he e u n d um casing 6. The s eel s uc u e 9 p essing o ce ac ing on he con eyo bel 3, which, due o he magni ude o he p essing o ce, is also p essed agains he casing o he e u n d um 6, is caused by he elec o-hyd aulic appa a us o he EP se ies 10 [ 17 , 37 ]. Due o he ic ion o ce in con ac wi h he con eyo bel su ace and wooden lining, he speed o he con eyo bel dec eases. As he p essu e o ce o he wooden lining ac ing agains he con eyo bel inc eases, he ic ional “b aking” o ce also inc eases linea ly, Machines 2023,11, 544 6 o 19 which causes a educ ion in he speed o he con eyo bel mo emen . A he momen when he ic ional o ce in he con ac su ace o he wooden lining and he con eyo bel eaches he magni ude o he ac i e o ce on he ci cum e ence o he d i ing d um casing, he mo ing con eyo bel s ops (i.e., by i s b aking). The labo a o y machine is equipped wi h an elec o-hyd aulic de ice 10 [ 37 ] achie ing a maximum a el heigh o 160 mm, a ac i e o ce o 1900 N, and an elec ic mo o wi h a powe consump ion o 450 W. Con eyo bel 3 in he lowe un is guided a ound he idle moun ed on he s eel s uc u e 7, which can slide e ically wi h mo emen ela i e o he s eel ame o he labo a o y de ice. To he lowe beam o he s eel ame s uc u e, as in 7, a s ain gauge load cell 8 [36] is a ached. The inal labo a o y de ice, see Figu e 3(o hese basic pa ame e s: heigh 1635 mm , leng h 2730 mm, wid h 780 mm, weigh app oxima ely 180 kg) equipped wi h load cells 5 and 8 enables he de ec ion and subsequen eco ding (using DEWESo X2 SP5 so - wa e [ 38 ]) o ins an aneous alues o he ensile o ce ac ing in he uppe un (T 1 [N]) and lowe (T 2 [N]) un o he endless loops o he con eyo bel 3 in ime [s] o he p o ided measu emen . Using he known (ob ained by measu ing on his labo a o y machine) magni udes o ensile o ces, we can calcula e, acco ding o he ela ionship (1), ic ion coe icien µ [-] a he slip poin ( α = β [deg]) be ween he con eyo bel and he d i ing d um. Machines 2023, 11, x FOR PEER REVIEW 7 o 20 Figu e 3. Labo a o y machine measu ing ensile o ces ac ing in he uppe and lowe uns o he con eyo bel . F om geome ic dimensions (Ri [m]) and he posi ion in he plane o (Hi [m], Li [m]) o d um axes 1, 2, and idle 3 (see Figu e 4), we can analy ically calcula e, o measu e using Au oCAD o SolidWo ks so wa e, he sizes o angles γ [deg] (5) and δ [deg] (6) o any e ical posi ion (i.e., o H1 [m] and H2 [m]) o he idle axes 3. Figu e 4. Con eyo bel guided in he uppe un o he labo a o y machine (a) unning om he idle 3 o he d i ing d um1 and (b) om he e u n d um 2 o he idle 3. HR R 112 γ = ε λ = a c g a csin [deg] L22 1L + H 11         −  −− , (5) R R2 H3 2 δ = ρ ω = a c g a csin [deg] L22 2L + H 22         −  −− , (6) I he magni ude o angles γ [deg] (5) and δ [deg] (6) a e known, we can, acco ding o he ela ionship Figu e 5, exp ess he magni ude o he ensile o ce in he con eyo bel in he uppe un o he labo a o y machine by (7), which de ines he magni ude o he acc uing o ce T1 [N] o he con eyo bel 3 on he d i ing d um 1. Figu e 3. Labo a o y machine measu ing ensile o ces ac ing in he uppe and lowe uns o he con eyo bel . F om geome ic dimensions (R i [m]) and he posi ion in he plane o (H i [m], L i [m]) o d um axes 1, 2, and idle 3 (see Figu e 4), we can analy ically calcula e, o measu e using Au oCAD o SolidWo ks so wa e, he sizes o angles γ [deg] (5) and δ [deg] (6) o any e ical posi ion (i.e., o H1[m] and H2[m]) o he idle axes 3. γ=ε−λ=a c gH1 L1−a csin  R1−R2 qL2 1+H2 1  [deg], (5) δ=ρ−ω=a c gH2 L2−a csin  R3−R2 qL2 2+H2 2  [deg], (6) I he magni ude o angles γ [deg] (5) and δ [deg] (6) a e known, we can, acco ding o he ela ionship Figu e 5, exp ess he magni ude o he ensile o ce in he con eyo bel in he uppe un o he labo a o y machine by (7), which de ines he magni ude o he acc uing o ce T1[N] o he con eyo bel 3 on he d i ing d um 1. Machines 2023,11, 544 7 o 19 Machines 2023, 11, x FOR PEER REVIEW 7 o 20 Figu e 3. Labo a o y machine measu ing ensile o ces ac ing in he uppe and lowe uns o he con eyo bel . F om geome ic dimensions (Ri [m]) and he posi ion in he plane o (Hi [m], Li [m]) o d um axes 1, 2, and idle 3 (see Figu e 4), we can analy ically calcula e, o measu e using Au oCAD o SolidWo ks so wa e, he sizes o angles γ [deg] (5) and δ [deg] (6) o any e ical posi ion (i.e., o H1 [m] and H2 [m]) o he idle axes 3. Figu e 4. Con eyo bel guided in he uppe un o he labo a o y machine (a) unning om he idle 3 o he d i ing d um1 and (b) om he e u n d um 2 o he idle 3. HR R 112 γ = ε λ = a c g a csin [deg] L22 1L + H 11         −  −− , (5) R R2 H3 2 δ = ρ ω = a c g a csin [deg] L22 2L + H 22         −  −− , (6) I he magni ude o angles γ [deg] (5) and δ [deg] (6) a e known, we can, acco ding o he ela ionship Figu e 5, exp ess he magni ude o he ensile o ce in he con eyo bel in he uppe un o he labo a o y machine by (7), which de ines he magni ude o he acc uing o ce T1 [N] o he con eyo bel 3 on he d i ing d um 1. Figu e 4. Con eyo bel guided in he uppe un o he labo a o y machine ( a ) unning om he idle 3 o he d i ing d um1 and (b) om he e u n d um 2 o he idle 3. Machines 2023, 11, x FOR PEER REVIEW 7 o 20 Figu e 3. Labo a o y machine measu ing ensile o ces ac ing in he uppe and lowe uns o he con eyo bel . F om geome ic dimensions (Ri [m]) and he posi ion in he plane o (Hi [m], Li [m]) o d um axes 1, 2, and idle 3 (see Figu e 4), we can analy ically calcula e, o measu e using Au oCAD o SolidWo ks so wa e, he sizes o angles γ [deg] (5) and δ [deg] (6) o any e ical posi ion (i.e., o H1 [m] and H2 [m]) o he idle axes 3. Figu e 4. Con eyo bel guided in he uppe un o he labo a o y machine (a) unning om he idle 3 o he d i ing d um1 and (b) om he e u n d um 2 o he idle 3. HR R 112 γ = ε λ = a c g a csin [deg] L22 1L + H 11         −  −− , (5) R R2 H3 2 δ = ρ ω = a c g a csin [deg] L22 2L + H 22         −  −− , (6) I he magni ude o angles γ [deg] (5) and δ [deg] (6) a e known, we can, acco ding o he ela ionship Figu e 5, exp ess he magni ude o he ensile o ce in he con eyo bel in he uppe un o he labo a o y machine by (7), which de ines he magni ude o he acc uing o ce T1 [N] o he con eyo bel 3 on he d i ing d um 1. Figu e 5. Con eyo bel in he uppe un o he labo a o y de ice. 1—d i ing d um, 2— e u n d um, 3—idle moun ed in a s eel s uc u e in he uppe un o he con eyo bel . Equa ion (7) is an app oxima ion based on he assump ion ha he ho izon al eac ion in he bea ings o cylinde 3 has been neglec ed. T1=FM1 sin(γ)+ g(δ)·cos(γ)[N], (7) In he e u n un, he ensile o ce T 2 [N] is applied in he con eyo bel , he magni ude o which is de e mined by hal he alue o he ensioning o ce F M2 [N], see Figu e 6a. The ension o ce is caused by he comp ession cylind ical sp ing 5 (see Figu e 6b) o known s i ness k s [N · m −1 ]. The ins an aneous alue o he pushing o ce F z [N] o he coil cylind ical sp ing 5 is eco ded by load cell 6. The ini ial alue o he sp ing comp essi e o ce 6 is adjus ed by igh ening he nu 7 moun ed on a h eaded od 8. Machines 2023, 11, x FOR PEER REVIEW 8 o 20 Figu e 5. Con eyo bel in he uppe un o he labo a o y de ice. 1—d i ing d um, 2— e u n d um, 3—idle moun ed in a s eel s uc u e in he uppe un o he con eyo bel . Equa ion (7) is an app oxima ion based on he assump ion ha he ho izon al eac- ion in he bea ings o cylinde 3 has been neglec ed. () ⋅ F M1 T = [N] 1sin γ + g(δ)cos(γ), (7) In he e u n un, he ensile o ce T2 [N] is applied in he con eyo bel , he magni- ude o which is de e mined by hal he alue o he ensioning o ce FM2 [N], see Figu e 6a. The ension o ce is caused by he comp ession cylind ical sp ing 5 (see Figu e 6b) o known s i ness ks [N·m−1]. The ins an aneous alue o he pushing o ce Fz [N] o he coil cylind ical sp ing 5 is eco ded by load cell 6. The ini ial alue o he sp ing comp essi e o ce 6 is adjus ed by igh ening he nu 7 moun ed on a h eaded od 8. Figu e 6. Tensioning he con eyo bel in he lowe un o he labo a o y equipmen (a) 2D ske ch, (b) using he cylind ical comp ession sp ing, (c) weigh s. 1— ans e d um, 2— ensioning d um, 3— e u n d um, 4—con eyo bel , 5—cylind ical sp ing, 6—load cell, 7—hexagon nu , 8— h eaded od, 9—weigh . The minimum magni ude o he cylind ical sp ing comp ession 5 (i.e., he gene a ion o comp ession o ce Fz [N]) du ing expe imen al measu emen s using he labo a o y equipmen mus be such o ensu e ha ensile o ce T2 [N] in he bel o he e u n un in he labo a o y machine eaches posi i e alues. Tensile o ce T2 [N] ope a ing on he e u n un o he con eyo bel can be gene a ed, apa om using he comp ession-cylind ical sp ing, by also using weigh FM2 [N], which is suspended on he axis o he ensioning d um, see Figu e 6c. A e he con eyo bel 3 (see Figu e 1) is se in mo ion a a speed ha is equal o he pe iphe ical speed [m·s−1] o he d i ing d um 1, an elec ic cu en is supplied o he elec o-hyd aulic de ice 10 [16], ex ending he pis on (a maximum ups oke o 160 mm). The ejec ing pis on, mechanically a ached o he s eel s uc u e o he b aking de ice 9, changes he posi ion o he ea pa o his s eel s uc u e, which pushes he b ake pad agains he ope a ing su ace o he con eyo bel 3 guided o e a e u n d um 6. In he con ac su ace o he con eyo bel 3 and he e u n d um casing 6, he ic ional o ce inc eases (wi h he inc easing p essu e o he b ake pad, which is caused by he pis on ejec ing om he elec o-hyd aulic de ice 10). This causes a g adual decele a ion o he speed o he con eyo bel 3 un il i s ops comple ely (i.e., = 0 m·s−1). Du ing he inc ease o he con eyo bel 3 comp ession o he e u n d um 6, he d i ing d um 1 is in ope a ion. Due o he ac i e o ce supplied by he d i e, he ac i e o ce is ans e ed by ic ion om he d i ing d um casing o he con eyo bel , wi h he w ap angle α [deg]. Figu e 7 displays he d i ing d um 1 and idle 4, a ound which he con eyo bel is guided. F om he known adii o d i ing d um R1 [m], idle R4 [m], and he dimensional pa ame e s o e ical H0 [m] and ho izon al L0 [m] dis ances o idle s axes om he d i - ing d um axis, we can use he ela ionship (8) and analy ically calcula e he angle ν [deg]. Figu e 6. Tensioning he con eyo bel in he lowe un o he labo a o y equipmen ( a ) 2D ske ch, ( b ) using he cylind ical comp ession sp ing, ( c ) weigh s. 1— ans e d um, 2— ensioning d um, 3— e u n d um, 4—con eyo bel , 5—cylind ical sp ing, 6—load cell, 7—hexagon nu , 8— h eaded od, 9—weigh . The minimum magni ude o he cylind ical sp ing comp ession 5 (i.e., he gene a ion o comp ession o ce F z [N]) du ing expe imen al measu emen s using he labo a o y equipmen mus be such o ensu e ha ensile o ce T 2 [N] in he bel o he e u n un in he labo a o y machine eaches posi i e alues. Machines 2023,11, 544 8 o 19 Tensile o ce T 2 [N] ope a ing on he e u n un o he con eyo bel can be gene a ed, apa om using he comp ession-cylind ical sp ing, by also using weigh F M2 [N], which is suspended on he axis o he ensioning d um, see Figu e 6c. A e he con eyo bel 3 (see Figu e 1) is se in mo ion a a speed ha is equal o he pe iphe ical speed [m · s −1 ] o he d i ing d um 1, an elec ic cu en is supplied o he elec o-hyd aulic de ice 10 [ 16 ], ex ending he pis on (a maximum ups oke o 160 mm). The ejec ing pis on, mechanically a ached o he s eel s uc u e o he b aking de ice 9, changes he posi ion o he ea pa o his s eel s uc u e, which pushes he b ake pad agains he ope a ing su ace o he con eyo bel 3 guided o e a e u n d um 6. In he con ac su ace o he con eyo bel 3 and he e u n d um casing 6, he ic ional o ce inc eases (wi h he inc easing p essu e o he b ake pad, which is caused by he pis on ejec ing om he elec o-hyd aulic de ice 10). This causes a g adual decele a ion o he speed o he con eyo bel 3 un il i s ops comple ely (i.e., = 0 m·s−1). Du ing he inc ease o he con eyo bel 3 comp ession o he e u n d um 6, he d i ing d um 1 is in ope a ion. Due o he ac i e o ce supplied by he d i e, he ac i e o ce is ans e ed by ic ion om he d i ing d um casing o he con eyo bel , wi h he w ap angle α[deg]. Figu e 7displays he d i ing d um 1 and idle 4, a ound which he con eyo bel is guided. F om he known adii o d i ing d um R 1 [m], idle R 4 [m], and he dimensional pa ame e s o e ical H 0 [m] and ho izon al L 0 [m] dis ances o idle s axes om he d i ing d um axis, we can use he ela ionship (8) and analy ically calcula e he angle ν[deg]. Machines 2023, 11, x FOR PEER REVIEW 9 o 20 Figu e 7. Con eyo bel guided o e he d i ing d um and con eyo idle o he labo a o y machine. 1—d i ing d um R1 = 108 mm, 4—idle R4 = 31.5 mm. LR R 014 ν = ψ τ = a c g a csin [deg] H22 0L + H 00         −  −− , (8) The eal size o he w ap angle α [deg] o he con eyo bel on he d i ing d um is di icul o measu e. The e o e, i is be e o calcula e he magni ude o angle α [deg] us- ing he ela ionship (9). Using Figu e 7, we can s a e ha he igh angle (π/2 = 90 deg) is de e mined by he sum o angles ν [deg] (8), α [deg] (9), and γ [deg] (5). Rela ionship (9) exp esses he ac ual alue o he w ap angle α [deg] o he con eyo bel ope a ing on he d i ing d um when bo h he e ical and ho izon al axes o he idle s 4 (see Figu e 7) and he idle placed in he holde ame 3 (see Figu e 3) a e dis an acco d- ing o he known alues om he axes o he d i ing d um 1. L HR R R R 0 112 14 α = 90 γ ν = 90 a c g a csin a c g a csin [deg] LH 22 22 10 L + H L + H 11 00    −             −  °− − °− − − − , (9) Technical s anda d [33] (p. 21) de ines wo main ypes o ubbe -g oo ed d um lin- ings: (a) Design A— he lining hickness is less han 20 mm wi h an a ow o c oss g oo e pa e n. The g oo e dep h is less han 6 mm; (b) Design B— he lining hickness is mo e han 20 mm. The g oo ing sys em is lis ed in [13,33]. The ecommended alues o ic ion coe icien s µ [-] depending on he d um su ace, he cleanliness o he con ac su aces, and con ac p essu e p [MPa] be ween he d um and bel wi h ubbe o e lays acco ding o [13,33] a e lis ed in Table 1. Table 1. Recommended alues o ic ion coe icien s µ [deg] o con eyo bel s wi h ubbe o e - lays. D um Su ace De- sign Condi ion o Con ac Su aces Con ac P es- su e p [MPa] F ic ion Coe i- cien µ [-] Smoo h s eel D y clean 0.0 ÷ 0.1 0.40 We clean 0.15 G oo ed ubbe D y clean 0.80 We clean 0.36 Figu e 7. Con eyo bel guided o e he d i ing d um and con eyo idle o he labo a o y machine. 1—d i ing d um R1= 108 mm, 4—idle R4= 31.5 mm. ν=ψ−τ=a c gL0 H0−a csin  R1−R4 qL2 0+H2 0  [deg], (8) The eal size o he w ap angle α [deg] o he con eyo bel on he d i ing d um is di icul o measu e. The e o e, i is be e o calcula e he magni ude o angle α [deg] using he ela ionship (9). Using Figu e 7, we can s a e ha he igh angle ( π /2 = 90 deg) is de e mined by he sum o angles ν[deg] (8), α[deg] (9), and γ[deg] (5). Rela ionship (9) exp esses he ac ual alue o he w ap angle α [deg] o he con eyo bel ope a ing on he d i ing d um when bo h he e ical and ho izon al axes o he idle s 4 (see Figu e 7) and he idle placed in he holde ame 3 (see Figu e 3) a e dis an acco ding o he known alues om he axes o he d i ing d um 1. α=90◦−γ−ν=90◦−a c gH1 L1−a csinR1−R2 √L2 1+H2 1−a c gL0 H0−a csinR1−R4 √L2 0+H2 0[deg],(9) Technical s anda d [ 33 ] (p. 21) de ines wo main ypes o ubbe -g oo ed d um linings: (a) Design A— he lining hickness is less han 20 mm wi h an a ow o c oss g oo e pa e n. The g oo e dep h is less han 6 mm; Machines 2023,11, 544 9 o 19 (b) Design B— he lining hickness is mo e han 20 mm. The g oo ing sys em is lis ed in [13,33]. The ecommended alues o ic ion coe icien s µ [-] depending on he d um su ace, he cleanliness o he con ac su aces, and con ac p essu e p [MPa] be ween he d um and bel wi h ubbe o e lays acco ding o [13,33] a e lis ed in Table 1. Table 1. Recommended alues o ic ion coe icien s µ [deg] o con eyo bel s wi h ubbe o e lays. D um Su ace Design Condi ion o Con ac Su aces Con ac P essu e p [MPa] F ic ion Coe icien µ[-] Smoo h s eel D y clean 0.0 ÷0.1 0.40 We clean 0.15 G oo ed ubbe D y clean 0.80 We clean 0.36 A he momen o b aking he con eyo bel on he e u n d um by an elec o-hyd aulic de ice, while he d i ing d um is in ope a ion, due o ibe ic ion in he con ac su ace o he con eyo bel and he d i ing d um casing, he ensile o ce in he uppe un inc eases and he ensile o ce in he e u ning bel un o he labo a o y equipmen dec eases. Tensile o ce F M1 [N] alue ac ing (on he con eyo idle moun ed in he ame s uc u e) in he uppe un o he con eyo bel du ing s eady unning and also du ing he b aking o he con eyo bel is de ec ed by he s ain gauge load cell 5 [ 36 ], see Figu e 1. The alues o ensile o ce F M1 [N] a e eco ded using DEWESo [ 38 ] so wa e du ing he ime o he expe imen al measu emen s. The magni ude o ensile o ce F M2 [N] in he lowe un o he con eyo bel aken du ing he en i e pe iod o expe imen al es ing is de ec ed by he s ain gauge load cell 8, see Figu e 1, and i is also eco ded using DEWESo [38] so wa e. I he powe o he elec ic mo o o he d i ing d um is high enough, hen when he bel b akes, he non-mo ing con eyo bel slips o e he su ace o he casing o he o a ing d i ing d um. A he momen o he bel slipping o e he ci cum e ence o he o a ing d um casing, we can use he g aphically plo ed cu es o measu ed ensile o ces (F M1 [N] and F M2 [N]) o calcula e he magni ude o he lea ing un o ce T2= FM2/2 [N] and acco ding o (7) he size o incoming un o ce T 1 [N]. T 2 = T M2 /2 [N] is an app oxima- ion close o eali y since he wo a ms o he bel a e no pa allel bu wi h an angle close o ze o. By knowing he ensile o ce a io o w ap angle α [deg] o he con eyo bel on he d i ing d um, we can use ela ionship (1) o calcula e he alue o he ic ion coe icien in mo ion µ[-]. 3. Resul s Expe imen al measu emen s p o ided on he labo a o y machine (Figu e 3) we e ca ied ou o ob ain a su icien numbe o measu ed alues o ensile o ces F M1 [N] (see Figu e 5) and F M2 [N] (see Figu e 6), which we e occu ing du ing b aking a a speed o [m·s−1] , p o ided by he con eyo bel and elec o-hyd aulic de ice [ 37 ] which he d i ing d um [34] was o a ing. G aphical cu es o measu ed ensile o ces om he aken measu emen s (see Figu e 8) using he men ioned labo a o y de ice we e eco ded using DEWESo [ 38 ] so wa e. The ime eco ding o he measu ed ensile o ces aken by bo h load cells (5 and 8 see Figu e 1) can be di ided in o 5 phases, see Figu e 8. Machines 2023,11, 544 16 o 19 The magni ude o he ic ion coe icien µ [-] ac ing be ween wo bodies on a mu ual con ac su ace canno be di ec ly measu ed. Howe e , i can be calcula ed using he magni udes o known o ces T 1 [N] and T 2 [N] and he magni ude o ic ion coe icien µ [-] on he slip limi o he bel placed on he d um, using he ela ionship (1). F ic ion in he bea ings o all he olling elemen s has been neglec ed. F om he alues measu ed o he ensile o ces ac ing on he labo a o y machine (Figu e 3), he magni udes o ic ion coe icien s in bo h d y and we condi ions o he wo con ac su aces we e calcula ed. These con ac su aces a e ep esen ed by a ubbe con eyo bel and he ubbe lining o he d i ing d um casing, and he ic ion coe icien s each highe alues han speci ied in he s anda d [33], see Table 1. The mean alue o he measu ed ic ion coe icien (see Table 2), aken when he su ace o he ubbe lining on he d i ing d um was d y, eaches he magni ude o µ = 0.85, co esponding o 106.3% o he s anda d alue. In cases when he su ace o he ubbe lining on he d i ing d um was we , he mean alue o he ic ion coe icien was µ = 0.43 (see Table 3), co esponding o 119.4% o he s anda d alue. This s anda d [ 33 ] does no de ine whe he he s a ed alues o he ic ion coe icien s a e measu ed as s a ic (a es ) o dynamic (in ope a ion) alues. The alues o he ic ion coe icien s measu ed on he ubbe lining as highe ones in compa ison wi h hose de ined by ele an s anda ds can be explained by he ac ha he su ace o he ubbe lining o he labo a o y machine d i ing d um, Figu e 12b, is no ideally smoo h bu oughened. The highe alues o ic ion coe icien s measu ed in we condi ions a e in luenced by he g oo es o med a ound he pe ime e o he ubbe lining, in o which he wa e is ex uded. This wa e comes om he con ac a ea be ween he ubbe lining and a pa o he con eyo bel placed on he d i ing d um. The highe measu ed alues o he ic ion coe icien s a e also due o he low pe iphe al speed o he d i ing d um, which o a es a he speed n b = 17.4 min −1 , compa ed o ope a ing speeds [ 21 ]. Values calcula ed o ic ion coe icien (Tables 2and 3), ac ing be ween he ubbe con eyo bel and he ubbe linings in a labo a o y machine, a e dynamic alues, which a e smalle in size compa ed o s a ic alues. Du ing expe imen al measu emen s ca ied ou on he labo a o y machine (Figu e 3) in ou labo a o y a he Depa men o Machine and Indus ial Design, Facul y o Mechanical Enginee ing, VSB-Technical Uni e si y o Os a a, he p essu e o ce ac ing on he con eyo bel was applied o he su ace o he ubbe lining (o o he s eel casing) o he d i ing d um. I s magni ude can be exp essed as he sum o ac ual (ob ained by measu emen s) ensile o ces T1(i) [N] and T2(i) [N]; see Table 2 o Table 4. The mean alue o he measu ed ic ion coe icien (see Table 4) when he su ace o he s eel casing o he d i ing d um is d y eaches he magni ude o µ = 0.5, co esponding o 125% o he s anda d alue. When he su ace o he s eel casing was we , he mean alue o he ic ion coe icien measu ed (see Table 5) eached µ = 0.41, co esponding o 273.3% o he s anda d alue. F om a physical poin o iew, he a ea be ween he d y and we s a e o he con ac su ace canno be de e mined. When he expe imen al measu emen s we e ca ied ou using ou labo a o y de ice, i was no clea how hick a laye o wa e was necessa y o undamen ally change he ic ion condi ions on he d i ing d um. An impo an ac ob ained ia he p o ided measu emen s is he knowledge ha i is e y di icul o de ine he s a e o he con ac a ea p ecisely. The ac ual alues o con ac p essu e, calcula ed acco ding o (4) o measu ed ensile o ces T 1(i) [N] and T 2(i) [N] on he labo a o y de ice, each alues o app ox. p= 20·103Pa o he ubbe linings on he d i ing d um. These con ac p essu es, when compa ed o he con ac p essu e used o bel con eyo s in p ac ice (p o 0.8 MPa), a e low. Unde labo a o y condi ions, he con ac p essu e alues o con ac p essu es, which show ubbe con eyo bel s used o bel con eyo s in indus y, can be di icul o achie e, as i would be necessa y o apply a high alue o ension o ce F M2 [N], see Figu e 6. E en lowe con ac p essu e alues, o app ox. p= 3.1 · 10 3 Pa was achie ed on he labo a o y machine o he Machines 2023,11, 544 17 o 19 s eel casing o he d i ing d um. Highe measu ed alues o he ic ion coe icien on he labo a o y machine a e also in luenced by he low con ac p essu e alues ( alues µ [-] dec ease wi h inc easing mean con ac p essu e be ween he bel and d um [27]). The mechanism (see 9 Figu e 1) b inging o es (by applying he con ac o ce o he wooden lining a ached o he b ake mechanism 9) he mo ing con eyo bel was no able o s op he bel wi h he w ap angle α [deg] agains he d i ing d um casing. By moun ing he idle 2, i was possible o change (lowe ) he w ap angle α [deg] o he con eyo bel on he labo a o y machine d i ing d um. The eal magni ude o he used w ap angle α [deg] o he con eyo bel on he d i ing d um casing (which can be aken as equal o he magni ude o he geome ic angle o he w ap) signi ican ly a ec s he ansmission capabili y. The eal size o he w ap angle α [deg] was calcula ed acco ding o he ela ionship (9), which is a ec ed by he dimensional pa ame e s o he labo a o y machine. I is necessa y o d aw a en ion o he ac ha he minimal change in he size o he w ap angle α[deg] leads o a signi ican in luence on he esul ing alue calcula ed using he ela ionship (1) o he ic ion coe icien µ[-]. The me hod o measu ing ensile o ces on ou labo a o y de ice, o which ins an a- neous alues ha e been de ec ed using s ain gauge load cells and displayed in DEWESo so wa e, is p esen ed in Sec ion 3 o his pape , and hei pu pose is o in oduce his labo a o y machine (see Figu e 3) on which, i is possible o p ac ically e i y he pa e ns o ac i e o ce ansmission by ic ion be ween he d i ing d um and he con eyo bel . Using he heo e ical Eule (Ey elwein) ela ionship (1), we can de e mine he ic ion coe icien p o ided ha a su icien amoun o lea ing o ce (a o ce ac ing in he e u n un o he endless loop o he con eyo bel ), ensu ing he ensioning o he bel by applying a p ope o ce, is gene a ed. 5. Conclusions In he case o a con inuously ope a ing con eyo de ice, namely he con eyo bel , he ansmission o he ci cum e en ial o ce om he d i ing d um casing o he con eyo bel is implemen ed using ic ion. Fo he ensile o ces in he con eyo bel , he Eule (Ey elwein) equa ion was applied o he ibe ic ion. The magni ude o he ansmi ed ci cum e en ial o ce om he d i e d um o he con eyo bel depends on he p es essing o he con eyo bel , he angle o w ap, and he ic ion coe icien ac ing be ween he bel and he d um casing. The ic ion coe icien ac ing be ween he bel and he d um casing a ies wi hin wide limi s unde ope a ing condi ions, especially o con eyo s ope a ing in open-ai a eas. The low alue o he ic ion coe icien makes i di icul o s a he con eyo and leads o he need o inc ease he w ap angle and implemen mul i-d um d i es. Since he ic ion coe icien in he con ac su ace o he con eyo bel and he d i ing d um casing canno be measu ed di ec ly, a labo a o y machine was cons uc ed on which he ensile o ces can be measu ed and he ic ion coe icien calcula ed om hem. The calcula ed alues o he ic ion coe icien s, gi en in Sec ion 3 o his a icle, canno be conside ed as being comple ely exac bu only as in o ma i e alues because he p esen ed esul s do no ake in o accoun all he ope a ing s a es unde which he ic ional o ce is ans e ed om he d i ing d um casing o he con eyo bel on eal con eyo s bel s. The labo a o y machine p esen ed in he a icle aims o ou line a possible me hodology, a ian , and p ocedu e, how (i he knowledge o he exac alue o he ic ion coe icien be ween he bel and d um is needed) i is possible o ob ain he alue o he ic ion coe icien om he calcula ions based on he measu ed ensile o ces. The calcula ed ac ual alue o he ic ion coe icien , used o a speci ic ype o con eyo bel and a ype o d i ing d um casing lining, can only be conside ed as eal i all pa ame e s o he speci ic con eyo bel a e aken in o accoun du ing he expe imen al es s, i.e., con eyo bel mo emen speed, ensioning o ce magni ude, he con ac p essu e alue be ween he bel and d i e d um. Machines 2023,11, 544 18 o 19 Au ho Con ibu ions: Concep ualiza ion, L.H.; me hodology, L.H.; so wa e, L.H. and J.F.; alida- ion, L.H.; o mal analysis, L.H. and P.N.; in es iga ion, L.H.; esou ces, L.H.; da a cu a ion, L.H. and P.N.; w i ing—o iginal d a p epa a ion, L.H.; w i ing— e iew and edi ing, L.H.; isualiza ion, L.H.; supe ision, J.F.; p ojec adminis a ion, J.F.; unding acquisi ion, L.H. 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 he Minis y o Educa ion, You h and Spo s o The Czech Republic, G an No. SP2023/003 and by he Minis y o Indus y and T ade o he Czech Republic, G an No. CZ.01.1.02/0.0/0.0/20_321/0024559. Ins i u ional Re iew Boa d S a emen : No applicable. In o med Consen S a emen : No applicable. Da a A ailabili y S a emen : The au ho s con i m ha he da a suppo ing he indings o his s udy a e a ailable wi hin he a icle. Acknowledgmen s: This wo k has been suppo ed by he Minis y o Educa ion, You h and Spo s o he Czech Republic om he Speci ic Resea ch P ojec SP2023/003 (SV3403351) and he Minis y o Indus y and T ade o he Czech Republic om he Speci ic Resea ch P ojec CZ.01.1.02/0.0/0.0/20_321/0024559 (MP342132). Con lic s o In e es : The au ho s decla e no con lic o in e es . Re e ences 1. An oniak, J. Theo e ical basis and indus ial applica ions o ene gy–sa ing and inc eased du abili y bel con eyo s. Ac a Mon an. Slo aca 2003,8, 150–157. 2. Webe , M.O.; Eh mann, A. Necessa y modi ica ion o he Eule –Ey elwein o mula o kni ing machines. J. Tex . Ins . 2012,103, 687–690. [C ossRe ] 3. Konyukho , A.; Shala, S. New benchma k p oblems o e i ica ion o he cu e- o-su ace con ac algo i hm based on he gene alized Eule –Ey elwein p oblem. In . J. Nume . Me hods Eng. 2022,123, 411–443. [C ossRe ] 4. Ha ada, T.; Hi osa o, K. 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