Study of the relationships between multi-hole, multi-disc mill performance parameters and comminution indicators

sus ainabili y A icle S udy o he Rela ionships be ween Mul i-Hole, Mul i-Disc Mill Pe o mance Pa ame e s and Comminu ion Indica o s We onika K uszelnicka 1,* , Jakub Hlos a 2, Jan Di iš 2and Łukasz Gie z 3   Ci a ion: K uszelnicka, W.; Hlos a, J.; Di iš, J.; Gie z, Ł. S udy o he Rela ionships be ween Mul i-Hole, Mul i-Disc Mill Pe o mance Pa ame e s and Comminu ion Indica o s. Sus ainabili y 2021,13, 8260. h ps://doi.o g/10.3390/ su13158260 Academic Edi o : Ada Ma ga ida Co eia Nunes Da Rocha Recei ed: 28 June 2021 Accep ed: 22 July 2021 Published: 23 July 2021 Publishe ’s No e: MDPI s ays neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a il- ia ions. Copy igh : © 2021 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/). 1Depa men o Machines and Technical Sys ems, Facul y o Mechanical Enginee ing, Uni e si y o Science and Technology in Bydgoszcz, al. P o . S. Kaliskiego 7, 85-796 Bydgoszcz, Poland 2ENET Cen e, Bulk Solids Cen e-Czech Republic, VSB-Technical Uni e si y o Os a a, 17. Lis opadu 15/2172, 708 33 Os a a, Czech Republic; [email p o ec ed] (J.H.); [email p o ec ed] (J.D.) 3Ins i u e o Machine Design, Facul y o Mechanical Enginee ing, Pozna´n Uni e si y o Technology, Pio owo 3, 60-965 Poznan, Poland; [email p o ec ed] *Co espondence: we [email p o ec ed] Abs ac : The knowledge o a g inde s uc u e, i s pe o mance pa ame e s and cha ac e is ics o bioma e ials b eakage a e c ucial o his esea ch whose aim is o de e mine he dependencies be ween pe o mance pa ame e s and comminu ion indica o s. The aim o his s udy is o in es iga e he ela ionships be ween mul i-disc mill pe o mance pa ame e s such as discs angula speed, ba ch dosing speed and comminu ion cha ac e is ics: powe consump ion, speci ic ene gy consump ion, h oughpu and size educ ion a io. To achie e hese goals, an expe imen was conduc ed on a i e-disc mill wi h a special moni o ing sys em. The esea ch p og am was es ablished, wi h disc angula speed a di e en con igu a ions and di e en ba ch dosing speeds. The esul s show ha powe consump ion, speci ic ene gy consump ion and size educ ion a io depend on he o al inc ease in angula speed o discs S ∆ω in such a way ha an inc ease in S ∆ω causes an inc ease in he abo emen ioned comminu ion indica o s. In u n, an inc ease in ba ch dosing speed Wcauses an inc ease in h oughpu . The i ing cu es o comminu ion indica o s in dependence o selec ed pe o mance pa ame e s a e also p esen ed in his s udy. Keywo ds: comminu ion; biomass; speci ic ene gy consump ion; size educ ion a io; e iciency 1. In oduc ion Comminu ion is a p ocess ha esul s in pa icle b eakage caused by he impac o he mill s uc u al elemen s and/o con ac s be ween mo ing (o en e y as ) pa icles [ 1 ]. As was s udied so a , comminu ion could be an e ec o c ushing, a i ion, cu ing, spli ing, bending, b eaking and hi ing [ 2 ]. The choice o he bes g inding me hod depends p ima ily on he p ope ies o he ma e ial o be comminu ed; o example, cu ing is ecommended o woody biomass while o b i le ma e ials, c ushing o impac comminu ion will be mo e sui able [3,4]. Due o he di e si y o ma e ials o be comminu ed and hei p ope ies, many ypes o comminu ion machines a e p oposed; o ins ance, ball mills, olle mills, disc mills, o a y shea s, d um mills, hamme mills and o he s [ 5 ]. Despi e signi ican echnological p og ess in he design o mills, he p oblem o hese machines is high ene gy consump ion and low e iciency [ 6 , 7 ]. To esol e his p oblem, he knowledge o he ela ions be ween s uc u al ea u es o he mills, he p ocess pa ame e s and he comminu ed ma e ial p ope ies is needed. Many s udies ha e deal wi h de e mina ion o dependencies be ween pa icle size and b eakage ene gy in s a ic and impac c ushing o single pa icles [ 8 – 11 ]. The e a e also s udies ha p esen he in luence o mul iple impac s on he b eakage ene gy [ 8 , 12 – 15 ]. The abo emen ioned app oaches p o ide da a on he na u e o he b eakage mechanism on he pa icle scale and can be used in he mill designing; howe e , hey do no p o ide Sus ainabili y 2021,13, 8260. h ps://doi.o g/10.3390/su13158260 h ps://www.mdpi.com/jou nal/sus ainabili y Sus ainabili y 2021,13, 8260 2 o 21 he in o ma ion on how a ma e ial will beha e inside he mill. This can be ob ained om expe imen al esea ch on mills a he p e-implemen a ion s age o p o ide esul s ha will help o imp o e mill design. In many s udies, he issues conce ning he ela ions o mill design and pe o mance pa ame e s on he comminu ion indica o s ha e been in es iga ed so a [ 16 – 20 ]. Resea ch in o olle p esses o mine al aw ma e ials g inding ha e shown ha he cou se o he g inding p ocess depends on he shape o he g inding chambe and g inding elemen s (e.g., su ace and s uc u e o g inding olle s) [ 21 ]. An impo an aspec a ec ing he g inding ene gy, e iciency and size educ ion a io is also he a io o he eed pa icle diame e o he in e - oll gap size ( hen, he cha ge ma e ial is compac ed and he o ces ac ing on he comminu ed ma e ial and mill elemen s inc ease) [ 21 , 22 ]. Desc ip ions o o ces ac ing on he comminu ed ma e ial ha e ound a pa icula applica ion in olle p esses o ha d and b i le aw ma e ials [ 22 ]. Reducing ene gy consump ion and imp o ing pe o mance was achie ed by c ea ing he so-called cascade sys ems in mul i- olle mills, whe e he cha ge ma e ial was subjec ed o b eakage se e al imes be ween a pai o olle s loca ed one abo e he ano he [ 23 – 25 ]. A emp s ha e been made o de e mine eliabili y models o olle mills based on ARIMA (au o eg essi e in eg a ed mo ing a e age) and HMM (Hidden Ma ko Model) models [ 26 ]. S udy [ 27 ] desc ibes, among o he s, he “in e pa icle b eakage” phenomenon occu ing in high p essu e olle p esses. The p essu e dis ibu ion on a olle su ace in he p essing zone has also been a subjec o esea ch [ 28 , 29 ]. Yang e al. [ 30 ] de e mined he op imal size o he in e - oll gap du ing milling o maize. The e a e se e al s udies which also discuss he ball mill pe o mance. No many s udies, howe e , add ess he connec ion be ween pe o mance pa ame e s and comminu ion indica o s o disc mills. Mos s udies o his aspec ha e been unde aken in Poland. A speci ic s uc u e o mul i-hole, mul i-disc mill has been p oposed and i has been ound ha his ype o mill is cha ac e ized by highe pe o mance and lowe ene gy consump ion han o he ypes o mills in ended o ce eals comminu ion. The so a conduc ed esea ch conce ns, among o he s, he impac o he mul i-disc mill design on he quali y o he p oduc , cha ge p ope ies, comminu ion e iciency, ela ions be ween he ma e ial p ope ies and comminu ion ene gy [ 31 – 35 ]. Unde s anding he ela ionships be ween he disc mo emen and he mass low is necessa y o unde s and he essence o he mul i-disc comminu ion p ocess and i s phenomena, as hey ha e a signi ican impac on he e iciency o comminu ion. The ene gy ela ions o mul i-disc comminu ion ha e al eady been desc ibed in he wo ks o J. Flizikowski [ 36 – 39 ]. The ela ionship be ween he mass low and he angle o he cha ge epose on he comminu ion e iciency in a i e-disc mills ha e been discussed in [ 40 – 42 ]. S udy [ 43 ] includes esul s o esea ch on mul i-disc comminu ion conce ning de e mina ion o he dependencies and e ec s o he mill s uc u al ea u es and physical–mechanical ea u es o he cha ge on he comminu ion indica o s, i.e., ene gy consump ion and quali y. In [ 41 , 44 – 46 ], he phenomenon o ope a ion i egula i y o mul i-disc mills is desc ibed. Dudziak analyzed he comminu ion p ocess e iciency in a supe sonic disc mill [ 47 ]. Yildi im e al. [ 48 ] in es iga ed he e ec o he disc gap size on he quali y o he p oduc , ene gy consump ion and e iciency. S udy [ 49 ] desc ibes ene gy losses in he o m o hea du ing comminu ion and he possibili y o i s eco e y. Zuñiga and Man a i conduc ed esea ch on dynamics o o ces ac ing on he comminu ed ma e ial and he wo king disc [11]. S udy [18] shows he machine and he p ocess ac o s in luencing he e iciency and he size educ ion a io indica ed on he basis o esea ch on a i e-disc mill. These ac o s include [ 18 ]: disc se ing in ela ion o he ho izon al plane, he me hod o eeding he ba ch ma e ial o he comminu ion chambe , he numbe o ixed and o a ing discs, geome y o he discs and holes in he discs, he o de o he discs wi h di e en geome y, he size o he in e -disc gap. The ene gy indica o s and en i onmen al assessmen o he comminu ion p ocess o a mul i-disc mill we e also p o ided. The in luence o angula eloci ies on he changes o hese indica o s was analyzed in s udies [50–52]. Sus ainabili y 2021,13, 8260 3 o 21 The li e a u e p o ides examples o se e al comminu ion indica o s [ 1 , 16 ], which can be classi ied in many ways, o example, as echnical, echnological and economic ones [ 53 ] o indica o s o quali y, e iciency and ha mlessness [ 54 ]. In gene al, comminu ion indica o s a e used o assess he pe o mance and e iciency o he comminu ion p ocess in di e en a eas. The mos equen ly used comminu ion indica o s a e powe consump ion, speci ic ene gy consump ion, h oughpu and size educ ion a io. F om he poin o iew o he comminu ion p oduc applica ion, he mos impo an a e indica o s connec ed wi h he ma e ial pa icle size a e comminu ion and size educ ion a io. The pa icle size a e comminu ion is usually desc ibed by s a is ical dependencies de e mined based on he pa icle size analysis by means o a sie e analysis o a dynamic imaging analysis. In hese me hods, he ma e ial is di ided in o size classes and he pe cen age o each size class is gene a ed in he whole sample. Based on hese esul s, he cumula i e size dis ibu ion and equency dis ibu ion o he pa icle size a e de e mined. To desc ibe he empi ical size dis ibu ions, se e al unc ions ha e been p oposed, o ins ance Ga es–Gaudin–Shuman (G.G.S) powe dis ibu ion, Rosin–Rammle dis ibu ion, log-no mal dis ibu ion, be a dis ibu ion o Kolmogo ow dis ibu ion [ 2 ]. They a e also equen ly used o ind dependencies be ween dis ibu ions pa ame e s o he pa icle size and he comminu ion p ocess pe o mance pa ame e s. These dis ibu ions can also be used o ind he cha ac e is ic pa icle size, o example, he a e age o median pa icle size which can be used o de e mine he size educ ion a io [55,56]. The s udies conduc ed so a [ 32 , 40 ] ha e p o en ha a highe size educ ion a io can be ob ained by inc easing he numbe o impac s o he comminu ion elemen s wi h he ma e ial pa icles; his, howe e , esul s in an ene gy consump ion inc ease [57–59]. An analysis o he s a e-o -a o he subjec leads o a conclusion ha he e is s ill no sys ema ic knowledge o he de elopmen o mul i-disc comminu ion and he ela ions be ween s uc u al ea u es, p ocess pa ame e s and pa icle b eakage. No p ecise ma he- ma ical models desc ibing ela ions be ween pe o mance pa ame e s and comminu ion indica o s ha e been de eloped ye . Gaining new knowledge o he g inde s design and hei ope a ional cha ac e is ics and bioma e ials b eakage cha ac e is ics is he ounda ion o he esea ch aimed a de e mina ion o he dependencies be ween pe o mance pa am- e e s and comminu ion indica o s. Simila dependencies and models ha e no ye been desc ibed o he analyzed mul i-hole, mul i-disc mills. A e iew ega ding he issues and models o comminu ion enginee ing con i ms he ele ance and impo ance o he unde aken esea ch. This includes bo h he p oduc quali y (e.g., ob aining he desi ed pa icles size a e comminu ion) and de e mina ion o indica o s o assessing he pe o mance o g anula biomass comminu ion sys ems. Resea ch in o hese issues di ec ed in his way can s imula e he de elopmen o echniques and me hods o g anula and ib ous bioma e ials g inding. Bea ing in mind he gaps in his kind o esea ch, his s udy is supposed o in es iga e he ela ionships be ween mul i-disc mill pe o mance pa ame e s such as discs angula speed, ba ch dosing speed and comminu ion cha ac e is ics: powe consump ion, speci ic ene gy consump ion, h oughpu and size educ ion a io. This s udy will p o ide answe s o he ollowing esea ch ques ions: (1) How will he in en ionally changed angula speed o discs in mul i-disc mill and speed o ba ch dosing a ec he powe consump ion, speci ic ene gy consump ion, h oughpu and size educ ion a io? (2) Wha alues o ope a ional pa ame e s will ensu e he occu ence o he possibly lowes powe consump ion and speci ic ene gy consump ion and possibly highes h oughpu and size educ ion a io? To achie e he goals, an expe imen was conduc ed on a i e-disc mill wi h a special moni o ing sys em. The esea ch p og am was es ablished o di e en disc angula speed con igu a ions and di e en ba ch dosing speeds. The comminu ion indica o s we e de e mined o each con igu a ion, and hen an analysis o he in luence o pe o mance pa ame e s on hese indica o s was ca ied ou Sus ainabili y 2021,13, 8260 4 o 21 2. Ma e ials and Me hods 2.1. Comminu ion Indica o s In his s udy, he mos commonly used indica o s including powe consump ion, speci ic ene gy consump ion, h oughpu and size educ ion a io ha e been de e mined. Powe consump ion is an indica o ha could be easily moni o ed based on di ec measu emen and i consis s o he powe o he machine powe uni idle un and he powe o e ec i e comminu ion, acco ding o equa ion [60,61]: P o =Pi+Pu(1) whe e: P u —powe consump ion o he ma e ial comminu ion in a gi en momen , kW, Pi—powe consump ion o he idle un in a gi en momen , kW. In many cases, he a e age o al powe consump ion is calcula ed o a ce ain ime in e al [52]: P o = n ∑ i=1P o i n(2) The nex impo an pa ame e , indica o o he comminu ion p ocess, which can be measu ed di ec ly and is necessa y in he assessmen o he p ocess and machine e iciency, is h oughpu (some imes called p oduc ion yield o simply e iciency). This indica o in o ms abou he mill pe o mance; i is abou he amoun o ma e ial ha is comminu ed in he speci ic ime ame, and i is exp essed as [62]: Q =∆m/∆ (3) whe e: ∆ m— he change in comminu ed ma e ial mass in ime in e al ∆ , ∆ —comminu ion ime in e al om 1 o 2. Equa ion (3) can ake he con inuous o m and hen he h oughpu is desc ibed by ela ionship [52]: Q =Z 0m d . (4) Gene ally, he powe consump ion and h oughpu a e connec ed. Usually, an inc ease in h oughpu causes an inc ease in powe consump ion. The indica o o speci ic ene gy consump ion (called also speci ic ene gy demand) is commonly used o compa ison o comminu ion machines. I gi es in o ma ion abou he amoun o ene gy consumed o comminu ion o a speci ied uni o ma e ial (mass o olume) [45,60,61,63,64]. I could be exp essed in wo ways: 1. as a a io o ene gy consump ion o he comminu ion and he mass (o olume) o ma e ial comminu ed: Eu=E o /m(5) 2. as a a io o a e age powe consump ion P o o h oughpu Q [62,64,65]: Eu =P o /Q (6) whe e: E u —speci ic ene gy consump ion, kWh · kg −1 ,E o — o al ene gy consump ion used o comminu ion o a speci ied po ion o ma e ial m, kWh. The size educ ion a io is conside ed as one o he comminu ion p oduc quali y indi- ca o s [ 63 , 66 ]. I desc ibes he ela ion be ween he cha ac e is ic sizes o he ma e ial be o e and a e comminu ion [ 67 , 68 ]. Depending on which cha ac e is ic pa icle dimensions will be adop ed, he ollowing exp ession o size educ ion a io can be p o ided: •o e all size educ ion a io [2]: λ=D/d(7) Sus ainabili y 2021,13, 8260 5 o 21 •limi size educ ion a io [2]: λl=Dmax/dmax (8) •a e age size educ ion a io [2]: λa=Da/da(9) •80% size educ ion a io [62]: λ80 =D80/d80 (10) whe e: D—equi alen diame e o he pa icles be o e comminu ion, mm, d—equi alen diame e o he pa icles a e comminu ion, mm, D max —a e age alue o he diame e s o he la ges pa icles o he c ushe ’s ba ch, mm, d max —a e age alue o he g inding p oduc la ges pa icle diame e , mm, D a —a e age dimension de e mined based on he weigh ed a e age o he eed a e age g ain, mm, d a —a e age dimension de e mined on he basis o he weigh ed a e age o he p oduc a e age g ain, mm, D 80 —dimension o he sie e hole, h ough which 80% o he eed ma e ial passes, d 80 —dimension o he sie e hole, h ough which 80% o he g inding p oduc passes. In his s udy, an 80% size educ ion a io was accep ed o he comminu ion assessmen . 2.2. Tes S and The esea ch was ca ied ou on he es s and p esen ed in he Figu e 1. Sus ainabili y 2021, 13, 8260 5 o 22 be o e and a e comminu ion [67,68]. Depending on which cha ac e is ic pa icle dimen- sions will be adop ed, he ollowing exp ession o size educ ion a io can be p o ided: • o e all size educ ion a io [2]: λ = D/d (7) • limi size educ ion a io [2]: λ l = D max /d max (8) • a e age size educ ion a io [2]: λ a = D a /d a (9) • 80% size educ ion a io [62]: λ 80 = D 80 /d 80 (10) whe e: D—equi alen diame e o he pa icles be o e comminu ion, mm, d—equi alen diame e o he pa icles a e comminu ion, mm, D max —a e age alue o he diame e s o he la ges pa icles o he c ushe ’s ba ch, mm, d max —a e age alue o he g inding p od- uc la ges pa icle diame e , mm, D a —a e age dimension de e mined based on he weigh ed a e age o he eed a e age g ain, mm, d a —a e age dimension de e mined on he basis o he weigh ed a e age o he p oduc a e age g ain, mm, D 80 —dimension o he sie e hole, h ough which 80% o he eed ma e ial passes, d 80 —dimension o he sie e hole, h ough which 80% o he g inding p oduc passes. In his s udy, an 80% size educ ion a io was accep ed o he comminu ion assess- men 2.2. Tes S and The esea ch was ca ied ou on he es s and p esen ed in he Figu e 1. Figu e 1. Tes s and o a mul i-disc g inde : 1—con ol uni , 2—mul i-disc g inde , 3—con ol cab- ine , 4—sc ew eede , 5—s ep mo o , 6— ecei ing baske , 7—scale. Adap ed om K uszelnicka, W. (2021) The s and consis s o he i e-disc mill RWT_KZ_5 (Uni e si y o Science and Tech- nology in Bydgoszcz, Bydgoszcz, Poland) and a con ol uni ADP 8080 (ADP, B zoza, Po- land). The mill is equipped wi h a hoppe wi h a sc ew eede d i en by a s eppe mo o , which enables one o con ol he speed o ba ch dosing. The comminu ion uni consis s o i e discs wi h holes (see Figu e 2) d i en by i e elec ic mo o s (each disc has i s own d i e mo o ) which allows o independen con ol o angula speed o each disc. The scale (ADP, B zoza, Poland) was ins alled below he ecei ing baske o measu ing he weigh o he comminu ed ma e ial. The in eg a ed pa o he esea ch s and is he sys em o pa icle size analysis consis ing o a high speed came a CMOS UI-1480SE-C-HQ (uEyeSE USB2.0 Came a, 1/2“ CMOS Colo Senso , 2560 × 1920 Pixel, Rolling/Global S a Figu e 1. Tes s and o a mul i-disc g inde : 1—con ol uni , 2—mul i-disc g inde , 3—con ol cabine , 4—sc ew eede , 5—s ep mo o , 6— ecei ing baske , 7—scale. Adap ed om K uszelnicka, W. (2021). The s and consis s o he i e-disc mill RWT_KZ_5 (Uni e si y o Science and Technol- ogy in Bydgoszcz, Bydgoszcz, Poland) and a con ol uni ADP 8080 (ADP, B zoza, Poland). The mill is equipped wi h a hoppe wi h a sc ew eede d i en by a s eppe mo o , which enables one o con ol he speed o ba ch dosing. The comminu ion uni consis s o i e discs wi h holes (see Figu e 2) d i en by i e elec ic mo o s (each disc has i s own d i e mo o ) which allows o independen con ol o angula speed o each disc. The scale (ADP, B zoza, Poland) was ins alled below he ecei ing baske o measu ing he weigh o he comminu ed ma e ial. The in eg a ed pa o he esea ch s and is he sys em o pa icle size analysis consis ing o a high speed came a CMOS UI-1480SE-C-HQ (uEyeSE USB2.0 Came a, 1/2“ CMOS Colo Senso , 2560 × 1920 Pixel, Rolling/Global S a Shu e , C-Moun , HQ-IR-Fil e , IDS Imaging De elopmen Sys ems Inc, Obe sulm, Ge many) wi h elecen ic lens TEC-55 (COMPUTAR, CBC G oup, Wa szawa Poland) and a ib a ing eede PL-2 (Wib ame , Koszalin, Poland) o ma e ial dosing in o he measu ing chambe . This sys em along wi h dedica ed so wa e o pa icle size and shape analysis ADP 8080 .2019.1 (ADP, B zoza, Poland) allows one o conduc he pa icle size analysis du ing comminu ion o a ba ch. Addi ionally, he s and was equipped wi h mois u e senso SHT71 (Sensi ion AG, S ae a ZH, Swi ze land) in he hoppe ( o ba ch mois u e con en measu emen ) and empe a u e senso s LM135 (Na ional Semiconduc o , San a Cla a, USA) o measu ing he ai empe a u e in he lab and he empe a u e o he mo o s. Sus ainabili y 2021,13, 8260 6 o 21 The con ol o he mill pe o mance pa ame e s such as disc angula speed and ba ch dosing speed is possible h ough he applica ion Młyn 2019 de eloped in LABView 2012 (Na ional Ins umen s, Aus in, TX, USA). The con ol panel o his applica ion is p esen ed in Figu e 3. The con ol sys em enables one o eco d and a chi e he changes in ime o mills pe o mance pa ame e s such as o ques, powe consump ion, angula speed o each disc, mois u e con en o a ba ch, p oduc weigh and pa icle size. Sus ainabili y 2021, 13, 8260 6 o 22 Shu e , C-Moun , HQ-IR-Fil e , IDS Imaging De elopmen Sys ems Inc, Obe sulm, Ge - many) wi h elecen ic lens TEC-55 (COMPUTAR, CBC G oup, Wa szawa Poland) and a ib a ing eede PL-2 (Wib ame , Koszalin, Poland) o ma e ial dosing in o he measu - ing chambe . This sys em along wi h dedica ed so wa e o pa icle size and shape anal- ysis ADP 8080 .2019.1 (ADP, B zoza, Poland) allows one o conduc he pa icle size anal- ysis du ing comminu ion o a ba ch. Addi ionally, he s and was equipped wi h mois u e senso SHT71 (Sensi ion AG, S ae a ZH, Swi ze land) in he hoppe ( o ba ch mois u e con en measu emen ) and empe a u e senso s LM135 (Na ional Semiconduc o , San a Cla a, USA) o measu ing he ai empe a u e in he lab and he empe a u e o he mo- o s. The con ol o he mill pe o mance pa ame e s such as disc angula speed and ba ch dosing speed is possible h ough he applica ion Młyn 2019 de eloped in LABView 2012 (Na ional Ins umen s, Aus in, TX, USA). The con ol panel o his applica ion is p e- sen ed in Figu e 3. The con ol sys em enables one o eco d and a chi e he changes in ime o mills pe o mance pa ame e s such as o ques, powe consump ion, angula speed o each disc, mois u e con en o a ba ch, p oduc weigh and pa icle size. Figu e 2. A scheme o he comminu ion uni s uc u al ea u es. Figu e 3. The con ol panel o he i e-disc mill. Figu e 2. A scheme o he comminu ion uni s uc u al ea u es. Sus ainabili y 2021, 13, 8260 6 o 22 Shu e , C-Moun , HQ-IR-Fil e , IDS Imaging De elopmen Sys ems Inc, Obe sulm, Ge - many) wi h elecen ic lens TEC-55 (COMPUTAR, CBC G oup, Wa szawa Poland) and a ib a ing eede PL-2 (Wib ame , Koszalin, Poland) o ma e ial dosing in o he measu - ing chambe . This sys em along wi h dedica ed so wa e o pa icle size and shape anal- ysis ADP 8080 .2019.1 (ADP, B zoza, Poland) allows one o conduc he pa icle size anal- ysis du ing comminu ion o a ba ch. Addi ionally, he s and was equipped wi h mois u e senso SHT71 (Sensi ion AG, S ae a ZH, Swi ze land) in he hoppe ( o ba ch mois u e con en measu emen ) and empe a u e senso s LM135 (Na ional Semiconduc o , San a Cla a, USA) o measu ing he ai empe a u e in he lab and he empe a u e o he mo- o s. The con ol o he mill pe o mance pa ame e s such as disc angula speed and ba ch dosing speed is possible h ough he applica ion Młyn 2019 de eloped in LABView 2012 (Na ional Ins umen s, Aus in, TX, USA). The con ol panel o his applica ion is p e- sen ed in Figu e 3. The con ol sys em enables one o eco d and a chi e he changes in ime o mills pe o mance pa ame e s such as o ques, powe consump ion, angula speed o each disc, mois u e con en o a ba ch, p oduc weigh and pa icle size. Figu e 2. A scheme o he comminu ion uni s uc u al ea u es. Figu e 3. The con ol panel o he i e-disc mill. Figu e 3. The con ol panel o he i e-disc mill. Sus ainabili y 2021,13, 8260 7 o 21 2.3. Tes Condi ions The in luence o he pe o mance pa ame e changes on comminu ion cha ac e is ics was in es iga ed du ing comminu ion o ice and co n g ains. Table 1p esen s he da a o g ain cumula i e pa icle size dis ibu ion be o e comminu ion ob ained in a g anulome ic analysis ca ied ou on a Camsize de ice (Re sch Technology GmbH, Haan, Ge many) acco ding o ISO s anda d 13322-2:2006 [ 69 ]. Volume based cumula i e pa icle size is desc ibed as [70]: Q3(xc_min, m)= m ∑ i=1 q3(xc_min,i)∆xc_min,i(11) whe e: Q 3 — he cumula i e size dis ibu ion, q3 — he a ea benea h he his og am, xc_min— he pa icle diame e , which is he sho es cho d o he measu ed se o he pa icle p ojec ion maximum cho ds. The same me hod was used o he ma e ial a e comminu ion. Table 1. The pa icle size dis ibu ion o ice and co n g ains be o e comminu ion. Rice Co n Size Class (mm) Q3(%) Size Class (mm) Q3(%) 0.000 1.000 0.0 0.000 3.350 0.0 1.000 1.180 0.0 3.350 4.000 0.1 1.180 1.400 0.1 4.000 4.750 1.8 1.400 1.700 8.4 4.750 5.600 9.0 1.700 2.000 56.5 5.600 6.700 2.7 2.000 2.360 97.0 6.700 8.000 72.1 2.360 2.800 98.8 8.000 9.500 10.0 2.800 3.350 99.6 3.350 4.000 100.0 The mois u e o g ains was de e mined using mois u e con en analyze MAC 210/NP (RADWAG, Radom, Poland), which ope a es unde a he mog a ime ic p inciple. The mois u e is de e mined based on he measu emen o he ma e ial weigh loss, by hea ing by halogen ligh . Samples weighing 5 g o ma e ial we e used. The analyze con inu- ously measu es he weigh s loss and calcula es he mois u e. The accu acy o he esul s in his case is 0.001%. The mois u e con en o co n g ains was 12.234% and o ice g ains 11.342%. Nex , 1 kg samples o ice and co n g ains we e p epa ed and comminu ed in he mill. The expe imen al p ocedu e is p og ammable; ha is, he pa ame e s we e chosen in such a way ha some dependencies can be obse ed. Independen a iables we e no andomly selec ed. Each expe imen di e ed in ba ch dosing speed and disc angula speed con igu a ion as p esen ed in Table 2. The o al inc ease o he disc angula speed S ∆ω , de ined as a sum o he angula speed inc ease on each disc om he lowes speed le el equal o 20 ad·s−1 a which ma e ial is comminu ed, was accep ed as a a iable, like in pape s [ 51 , 52 ], o in es iga e he in luence o he disc angula speed changes on he com- minu ion indica o s such as powe consump ion, speci ic ene gy consump ion, h oughpu and size educ ion a io. Du ing comminu ion, he o ques, powe consump ion, angula speed o each disc, mois u e con en o ba ch, p oduc weigh and pa icle size we e eco ded wi h sampling equency o 0.5 s and a chi ed. Based on he eco ded pa am- e e s, he comminu ion indica o s—powe consump ion, speci ic ene gy consump ion, h oughpu and size educ ion a io—we e de e mined. Sus ainabili y 2021,13, 8260 8 o 21 Table 2. Tes ed con igu a ions o ba ch dosing speed and comminu ion disc eloci ies. W S∆ω∆ωω1ω2ω3ω4ω5 kg·h−1 ad·s−1 ad·s−1 ad·s−1 ad·s−1 ad·s−1 ad·s−1 ad·s−1 100 200 20 100 80 60 40 20 150 15 80 65 50 35 20 100 10 60 50 40 30 20 50 5 40 35 30 25 20 80 200 20 100 80 60 40 20 150 15 80 65 50 35 20 100 10 60 50 40 30 20 50 5 40 35 30 25 20 60 200 20 100 80 60 40 20 150 15 80 65 50 35 20 100 10 60 50 40 30 20 50 5 40 35 30 25 20 40 200 20 100 80 60 40 20 150 15 80 65 50 35 20 100 10 60 50 40 30 20 50 5 40 35 30 25 20 ω1 , ω2 , ω3 , ω4 , ω5 —angula speeds o discs, ∆ω —inc ease in angula speeds, S ∆ω — o al inc ease in angula speeds. 2.4. S a is ical Analysis A s a is ical analysis o he esul s in ol ed he co ela ion analysis, mul iple linea eg ession analysis and polynomial i ing. Fo he s a is ical analysis, he O igin P o 2021b (O iginLab Co po a ion, No hamp on, MA, USA) so wa e was used. Fi s , he co ela ion o he independen and dependen a iables was pe o med using he Pea son co ela ion analysis and nex , he pa ial co ela ion analysis, i s choosing he ba ch dosing speed and secondly he o al inc ease in disc angula speeds as a con ol a iable. The co ela ion analysis was done o in es iga e he in luence o he independen a iable on he dependen a iables, and pa ial co ela ion analysis o check he in luence o a single a iable, excluding he e ec o he second a iable on he dependen a iables. The signi icance le el was accep ed o be p< 0.1 o bo h analyses. A e co ela ion analysis, a mul iple linea eg ession was pe o med o build and check he accu acy o he dependen a iable p edic ion models. The models and he model coe icien s we e ound o be signi ican o p< 0.05. Nex , he polynomial i ing unc ions was buil , o check he accu acy o models o he han linea , which can be used o desc ip ions o he ela ions be ween he mill pe o mance pa ame e s and comminu- ion indica o s. Di e en polynomial models we e es ed and he maximum deg ee o independen a iables was se o h ee. The i ing o he models was anked based on he BIC c i e ion and de e mina ion coe icien R 2 . The bes i ed model was he one o which R2was g ea e han 0.5 and BIC assumed he lowes alue. 3. Resul s 3.1. Values o Comminu ion Indica o s Figu es 4–7shows he alues o comminu ion indica o s: powe consump ion, h ough- pu , speci ic ene gy consump ion and size educ ion a io o he es ed con igu a ion o disc speed and ba ch dosing speed, acco ding o Table 2. Sus ainabili y 2021,13, 8260 9 o 21 Sus ainabili y 2021, 13, 8260 9 o 22 ice. I can be obse ed ha du ing comminu ion o ice and co n gains, he powe con- sump ion is inc easing along wi h a disc speed inc ease and, in e ec , he o al inc ease in disc angula speed. Powe consump ion dec eases along wi h a dec ease o ba ch dosing speed du ing comminu ion o ice. This s a emen is only pa ially ue o co n commi- nu ion. Based on he esul s p esen ed in Figu e 4b, powe consump ion was dec easing along wi h he ba ch dosing speed dec ease only o S∆ω = 200 ad·s −1 and S∆ω = 150 ad·s −1 . Fo o he le els o S∆ω he dependence be ween powe consump ion and ba ch dosing speed is no clea . (a) (b) Figu e 4. Powe consump ion du ing comminu ion on i e-disc mill: (a) ice; (b) co n. The second de e mined indica o was h oughpu , calcula ed acco ding o Equa ion (3) on he basis o mass measu emen in he ecei ing baske . The highes h oughpu o ice comminu ion appea s when S∆ω = 150 ad·s −1 and W = 100 kg·h −1 ; he lowes , o S∆ω = 100 ad·s −1 and W = 40 kg·h −1 . Du ing he expe imen wi h co n, he highes h oughpu was no ed o S∆ω = 150 ad·s −1 and W = 60 kg·h −1 , while he lowes was o S∆ω = 50 ad·s −1 and W = 40 kg·h −1 . Based on he esul s p esen ed in Figu e 5, i is ha d o ind any egu- la i ies in h oughpu changes wi h changes o pe o mance pa ame e s. Howe e , i can be seen ha h oughpu was dec easing wi h he ba ch dosing speed dec ease o he disc speed se ing o which S∆ω was equal o 150 ad·s −1 and 100 ad·s −1 o ice comminu ion and 200 ad·s −1 and 100 ad·s −1 o co n p ocessing. In expe imen s wi h ice, i was ound ha dec easing he disc speed (S∆ω ge ing smalle alues) when W = 40 kg·h −1 causes a dec ease in h oughpu , while in he expe imen wi h co n, dec easing he disc speed e- sul s in h oughpu inc ease when W = 80 kg·h −1 . Figu e 4. Powe consump ion du ing comminu ion on i e-disc mill: (a) ice; (b) co n. Sus ainabili y 2021, 13, 8260 10 o 22 (a) (b) Figu e 5. Th oughpu du ing comminu ion on i e-disc mill: (a) ice; (b) co n. Speci ic ene gy consump ion was calcula ed acco ding o Equa ion (5) o each es ed con igu a ion o pe o mance pa ame e s and he esul s a e p esen ed inFigu e 6. The lowes alue o speci ic ene gy consump ion occu ed o S∆ω = 50 ad·s −1 , W = 60 kg·h −1 and S∆ω = 150 ad·s −1 , W = 40 kg·h −1 , espec i ely, o ice and co n comminu ion. In u n, he highes alue o speci ic ene gy consump ion was ound o S∆ω = 150 ad·s −1 , W = 40 kg·h −1 and S∆ω = 200 ad·s −1 , W = 40 kg·h −1 o ice and co n comminu ion, espec i ely. Based on he p esen ed esul s, some egula i ies can be s a ed. Gene ally, in he case o ice and co n comminu ion inc ease along wi h he disc speed, which is equi alen o o al inc ease in angula speeds S∆ω esul s in speci ic ene gy consump ion inc ease. (a) (b) Figu e 6. Speci ic ene gy consump ion du ing comminu ion on i e-disc mill: (a) ice; (b) co n. The las analyzed comminu ion indica o was 80% size educ ion a io calcula ed ac- co ding o Equa ion (10) based on he dimensions o pa icle size dimensions measu ed be o e and a e comminu ion. The size educ ion a io was highe in he case o co n comminu ion han o ice (Figu e 7). The highes alue o size educ ion a io occu ed o S∆ω = 220 ad·s −1 , W = 100 kg·h −1 and S∆ω = 200 ad·s −1 , W = 80 kg·h −1 o ice and co n comminu ion, espec i ely. The lowes alues we e eco ded o S∆ω = 50 ad·s −1 , W = 80 kg·h −1 and S∆ω = 100 ad·s −1 , W = 40 kg·h −1 . I can be obse ed ha he size educ ion a io dec eases wi h a dec ease in o al g adien o angula speed o discs S∆ω. Figu e 5. Th oughpu du ing comminu ion on i e-disc mill: (a) ice; (b) co n. Sus ainabili y 2021, 13, 8260 10 o 22 (a) (b) Figu e 5. Th oughpu du ing comminu ion on i e-disc mill: (a) ice; (b) co n. Speci ic ene gy consump ion was calcula ed acco ding o Equa ion (5) o each es ed con igu a ion o pe o mance pa ame e s and he esul s a e p esen ed inFigu e 6. The lowes alue o speci ic ene gy consump ion occu ed o S∆ω = 50 ad·s −1 , W = 60 kg·h −1 and S∆ω = 150 ad·s −1 , W = 40 kg·h −1 , espec i ely, o ice and co n comminu ion. In u n, he highes alue o speci ic ene gy consump ion was ound o S∆ω = 150 ad·s −1 , W = 40 kg·h −1 and S∆ω = 200 ad·s −1 , W = 40 kg·h −1 o ice and co n comminu ion, espec i ely. Based on he p esen ed esul s, some egula i ies can be s a ed. Gene ally, in he case o ice and co n comminu ion inc ease along wi h he disc speed, which is equi alen o o al inc ease in angula speeds S∆ω esul s in speci ic ene gy consump ion inc ease. (a) (b) Figu e 6. Speci ic ene gy consump ion du ing comminu ion on i e-disc mill: (a) ice; (b) co n. The las analyzed comminu ion indica o was 80% size educ ion a io calcula ed ac- co ding o Equa ion (10) based on he dimensions o pa icle size dimensions measu ed be o e and a e comminu ion. The size educ ion a io was highe in he case o co n comminu ion han o ice (Figu e 7). The highes alue o size educ ion a io occu ed o S∆ω = 220 ad·s −1 , W = 100 kg·h −1 and S∆ω = 200 ad·s −1 , W = 80 kg·h −1 o ice and co n comminu ion, espec i ely. The lowes alues we e eco ded o S∆ω = 50 ad·s −1 , W = 80 kg·h −1 and S∆ω = 100 ad·s −1 , W = 40 kg·h −1 . I can be obse ed ha he size educ ion a io dec eases wi h a dec ease in o al g adien o angula speed o discs S∆ω. Figu e 6. Speci ic ene gy consump ion du ing comminu ion on i e-disc mill: (a) ice; (b) co n. Sus ainabili y 2021,13, 8260 16 o 21 educ ion a io depend on he o al inc ease in disc angula speed S ∆ω in such a way ha he inc ease in S ∆ω causes an inc ease in he conside ed comminu ion indica o s. In u n, an inc ease in ba ch dosing speed Wcauses an inc ease in h oughpu , as he ob ained a e age and high posi i e co ela ions sugges (Tables 3–5). In he pa ial co ela ion analysis, when ba ch dosing speed was selec ed as a con- olling a iable, he alues o co ela ion coe icien s be ween a iables (Tables 4and 5) we e sligh ly highe han hose ob ained om Pea son analysis (Table 3), which sugges s ha he alues o powe consump ion, speci ic ene gy consump ion and size educ ion a io depend mos ly on o al inc ease in disc angula speeds and subsequen ly on he disc speed. When o al inc ease in disc angula speeds was selec ed as a con olling a iable, posi i e co ela ions appea ed be ween ba ch dosing speed and h oughpu o bo h com- minu ed gains and be ween ba ch dosing speed and powe consump ion in he case o ice comminu ion. The abo e ela ions a e in line wi h he esul s o o he mills p esen ed in s ud- ies [ 16 , 56 , 62 , 72 – 76 ]. The ela ion be ween powe consump ion and o al inc ease in disc angula speed is a esul o a simple dependence ha powe is he p oduc o o que and angula speed mul iplica ion, which o idle un o he mul i-disc mill (wi hou ba ch) is a linea dependance and is mo e han hal o he o al powe equi emen , e en o a ba ch loaded mill as was p esen ed in [ 77 ]. Many s udies show ha powe consump ion is i egula du ing comminu ion, which is caused by i egula low o he ma e ial in he comminu ion chambe and mo emen i egula i y o milling elemen s [ 40 , 41 , 46 ]. I appea s as a pe iodical inc ease and dec ease in powe consump ion in ime. The a i- abili y o powe o ba ch dosed comminu ion chambe is an e ec o disc mo emen i egula i ies, i egula i ies o he eede mo emen and i egula i ies o he ma e ial low inside he chambe desc ibed in [ 41 , 45 , 46 ]. This causes ha du ing each obse a ion, a di e en amoun o ma e ial is comminu ed (di e en cu ing and c ushing esis ance appea s). Highe powe consump ion o co n comminu ion han o ice g inding esul s om he di e ences in he g ain size, s uc u e and mechanical p ope ies. As desc ibed ea lie [ 78 , 79 ], highe o ces and ene gy a e needed o b eak he co n g ains han ice g ains. In he case o ice comminu ion, he powe consump ion depends also on he ba ch dosing speed W. Gene ally, his dependance is qui e ob ious; he mo e ma e ial be ween he discs, he la ge o ce (powe ) is needed o b eak he g ains. Howe e , o co n comminu ion, his dependence has no been con i med. I should be no ed ha he amoun o ma e ial ha unde goes comminu ion is no only he e ec o he ba ch dosing speed bu also he olume o ma e ial ha could be inse ed in o he disc mill holes. This amoun is dependen on he o al olume o holes and angula speed, which de e mine he hole illing ime. This ype o ma e ial dosing in ol es pe iodical dosing, ha is, di e en ma e ial amoun s a e be ween he discs in a gi en ime in e al. The p esence o a posi i e co ela ion be ween ba ch dosing and powe consump ion in he case o ice comminu ion and he absence o such a ela ion in he case o co n comminu ion can be a esul o physical–mechanical p ope ies o g ains. The ice g ains a e smalle and can be easie p essed in o he disc holes (mo e g ans will all in o he holes) han co n g ains. In his case, also he lowabili y o gains is impo an . In p ac ice, o dec ease he powe consump ion, a lowe angula speed o disc should be applied. The h oughpu was ound o be dependen only on ba ch dosing speed (Figu e 5, Tables 3–5). This ela ion can be easily jus i ied; he mo e ma e ial is dosed, he mo e is comminu ed. Howe e , he ob ained esul s (Figu e 5) and he alues o co ela ion coe icien s (Tables 3–5) sugges ing only a e age and high co ela ions lead o a conclusion ha he e a e some co ounde s ha dis up he low o ma e ial inside he mill. The a iabili y o h oughpu can be caused by he ma e ial s uc u e, i s mois u e con en and he adhesi e abili ies o pa icles. We pa icles wi h he adhesi e p ope ies will cause p oblems wi h he ma e ial low [ 80 – 83 ], because agglome a es will be c ea ed and some ma e ial will s ick o he discs and walls o he comminu ion chambe . This makes some pa o he ma e ial emain in he g inding chambe , and he e may also be momen s when Sus ainabili y 2021,13, 8260 17 o 21 he esidual ma e ial peels o , causing ab up inc eases in e iciency, which was u he desc ibed in [ 41 , 45 , 46 ]. When analyzing he h oughpu alues (Figu e 5), i should be s a ed ha hey did no exceed 40 kg · h −1 , which leads o he conclusion ha wi h he numbe and size o holes used and he ange o angula eloci ies o he i s disc, despi e using eede capaci ies highe han 40 kg · h −1 , he mill will no be able o achie e highe capaci ies. Thus, in o de o imp o e he pe o mance, he disc design should be modi ied, i.e., he o al olume o holes in he discs should be inc eased. The lack o dependance o he h oughpu on he o al inc ease in disc angula speed could be he e ec o a small ange o disc angula speed o al inc eases and he exis ence o di e en pai s o angula eloci y –ba ch dosing speed, which will ensu e he maximum h oughpu o a gi en le el o ba ch dosing. The speci ic ene gy consump ion was posi i ely co ela ed wi h he o al inc ease o he angula speed o he disc (Tables 3–5). By de ini ion (Equa ion (6)), he speci ic ene gy consump ion depends on he powe consump ion and h oughpu . Powe consump ion was s ongly co ela ed wi h S ∆ω , while he h oughpu was mode a ely co ela ed wi h he ba ch dosing speed; hence, a mode a e and high co ela ion wi h S ∆ω and a lack o co ela ion wi h he ba ch dosing speed esul . The 80% size educ ion a io was ound o be dependen only on he o al inc ease o disc angula speed (see Figu e 7, Tables 3–5). A s ong posi i e co ela ion occu ed ( R2> 0.89 ). The ob ained ela ion is simila o ha p esen ed in [ 52 , 84 – 86 ]. The inc ease in he size educ ion a io wi h he inc ease o S ∆ω esul s om a highe numbe o con ac s be ween he ma e ial and comminu ion elemen s occu ing o highe angula eloci ies. The e we e no s a is ically signi ican co ela ions be ween size educ ion a io and ba ch dosing speed, so he ela ion ob ained o a s i ed mill, ha is, he g ain ineness inc ease wi h he eed a e dec ease p esen ed in [ 86 ], was no con i med. The lack o s a is ical dependence may be due o he ac ha only ou a es o ba ch dosing we e es ed in his s udy. Due o he ac ha he size educ ion a io did no co ela e wi h he ba ch dosing speed, he i ed cu es desc ibing changes in size educ ion a io we e unc ions o one a iable, namely, S∆ω. Fu he esea ch should be ocused on iden i ica ion o he low inside he mul i-hole, mul i-disc mill wi h he use o he disc e e elemen modeling, which will help one o look inside he comminu ion chambe and iden i y any ma e ial blockage. Ano he s udy ha should be conduc ed is o de e mine he bes a io be ween he comminu ed pa icle size and he dosed ma e ial olume and he numbe and diame e o holes in he subsequen discs so as o ensu e he highes possible h oughpu and elimina e he p oblems wi h he ma e ial low h ough he holes. 5. Conclusions Based on he esea ch esul s, he ollowing conclusions can be d awn: • Powe consump ion, speci ic ene gy consump ion and size educ ion a io o mul i- hole, mul i-disc comminu ion depend on he o al inc ease in angula speed o discs S ∆ω in such a way ha he inc ease o S ∆ω causes an inc ease in he analyzed comminu ion indica o s; •An inc ease in ba ch dosing speed Wcauses an inc ease in h oughpu ; • The a iabili y o h oughpu can be caused by he ma e ial s uc u e o he ma e ial, i s mois u e con en and he adhesi e abili ies o pa icles; • In o de o imp o e he pe o mance, he design o he disc should be modi ied, i.e., he o al olume o holes in he discs should be inc eased, • Fu he esea ch should ocus on iden i ica ion o he low inside he mul i-hole, mul i-disc mill wi h he use o disc e e elemen modeling; • I is necessa y o de e mine he bes a io be ween he comminu ed pa icle size, he dosed ma e ial olume and he numbe and diame e o holes in he subsequen discs o imp o e he mill pe o mance; Sus ainabili y 2021,13, 8260 18 o 21 • The size educ ion a io o ice and co n comminu ion and powe consump ion du ing co n size educ ion can be p edic ed using he models o one a iable— o al inc ease o discs speed, while o he indica o s can be p edic ed by models o wo a iables— o al inc ease o discs speed and ba ch dosing speed. Supplemen a y Ma e ials: The ollowing a e a ailable online a h ps://www.mdpi.com/a icle/ 10.3390/su13158260/su13158260/s1, Table S1: Ranks o es ed polynomial i ing cu es o powe consump ion du ing ice comminu ion as a unc ion o ba ch dosing speed W and o al inc ease in angula speeds S ∆ω , Table S2: Ranks o es ed polynomial i ing cu es o powe consump ion du ing co n comminu ion as a unc ion o ba ch dosing speed W and o al inc ease in angula speeds S ∆ω , Table S3: Ranks o es ed polynomial i ing cu es o h oughpu du ing ice comminu ion as a unc ion o ba ch dosing speed W and o al inc ease in angula speeds S ∆ω , Table S4: Ranks o es ed polynomial i ing cu es o h oughpu du ing co n comminu ion as a unc ion o ba ch dosing speed W and o al inc ease in angula speeds S ∆ω , Table S5: Ranks o es ed polynomial i ing cu es o speci ic ene gy consump ion du ing ice comminu ion as a unc ion o ba ch dosing speed W and o al inc ease in angula speeds S ∆ω , Table S6: Ranks o es ed polynomial i ing cu es o speci ic ene gy consump ion du ing co n comminu ion as a unc ion o ba ch dosing speed W and o al inc ease in angula speeds S ∆ω , Table S7: Ranks o es ed polynomial i ing cu es o size educ ion a io du ing ice comminu ion as a unc ion o ba ch dosing speed W and o al inc ease in angula speeds S ∆ω , Table S8: Ranks o es ed polynomial i ing cu es o size educ ion a io du ing co n comminu ion as a unc ion o ba ch dosing speed Wand o al inc ease in angula speeds S∆ω. Au ho Con ibu ions: Concep ualiza ion, W.K.; me hodology, W.K., J.H., J.D. and Ł.G.; so wa e, W.K., J.H. and J.D.; alida ion, W.K., J.H., J.D. and Ł.G.; o mal analysis, W.K., J.H., J.D. and Ł.G.; in es iga ion, W.K.; esou ces, W.K.; da a cu a ion, W.K.; w i ing—o iginal d a p epa a ion, W.K.; w i ing— e iew and edi ing, W.K., J.H., J.D. and Ł.G.; isualiza ion, W.K., J.H., J.D. and Ł.G.; supe ision, W.K.; p ojec adminis a ion, W.K.; unding acquisi ion, W.K. All au ho s ha e ead and ag eed o he published e sion o he manusc ip . Funding: Scien i ic wo k was inanced by he budge esou ce o science in 2017–2021, as a esea ch p ojec unde he “Diamen owy G an ” p og am. This esea ch was unded by he Minis y o Science and Highe Educa ion o Poland, g an numbe DI2016 001646. 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 da a p esen ed in his s udy a e a ailable on eques om he co esponding au ho . 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