6 th International Conference on Trends in Agricultural Engineering 7-9 September 2016, Prague, Czech Republic

Transcription

1 THEORETICAL INVESTIGATIONS OF MINERAL FERTILISER DISTRIBTION BY MEANS OF AN INCLINED CENTRIFGAL TOOL V. Bulgakv 1, O. Adamchuk, S. Ivanvs 3 1 Nainal niversiy Lie and Envirnmenal Sciences kraine Nainal Scieniic Cenre kraine Insiue r Agriculural Engineering 3 Lavia niversiy Agriculure Absrac A presen a grea pa mineral erilisers is inrduced by means machines equipped wih cenriugal spreading ls. One pssible sluins heir imprvemen wards unirm eriliser disribuin arund he surace he ield is he use cenriugal spreading ls wih heir axes rain being inclined a an angle he hriznal plane. Thereical invesigains have been cnduced and a new equain bained describing he mvemen a maerial paricle a eriliser alng he blade he cenriugal l, aking in accun he inclinain angle he spreading disk; and is sluin is given in a clsed rm. The research was carried u wih he use he mehds hereical mechanics and numerical esimains n he PC. Thereical dependencies have been deermined in rde ind u abslue velciy he paricles erilisers a he mmen hey leave he spreading disk. The use he revealed dependencies and heir subsequen numerical sluin n he PC prvided a pssibiliy esablish he impac he design and kinemaic parameers, he perainal cndiins he inclined cenriugal disribur, paricularly, he value abslue velciy he eriliser paricles leaving he disribur disk and heir accelerain angle. ey wrds: dierenial eriliser, cenriugal spreading, abslue velciy. INTRODCTION The prducin eiciency varius agriculural crps depends a cnsiderable degree n he applicain mineral erilisers, ms en inrduced n he ield by he surace mehd spreading hem using machines equipped wih cenriugal spreading ls, were described by BIOCCA (013). The use hese machines has indispuable advanages ver he her similar machines. Ye hey need urher imprvemen, which cncerns, irs all, he unirmiy eriliser disribuin arund he surace he ield and depends n he design and kinemaic parameers heir peraing ls. I is well-knwn ha he wrking widh he machine r he applicain mineral erilisers by a cenriugal mehd depends n he value abslue velciy spreading l and angle erilisers leaving he surace is beween he vec he laer and he hriznal plane. Value depends n he gemeric parameers and he kinemaic cndiins he perain he cenriugal spreading l, as well as n physical and mechanical prperies mineral erilisers. As a resul earlier cnduced invesigains, pimisain he gemeric parameers he cenriugal spreading l was carried u, aking in accun he physical and mechanical prperies mineral erilisers, were described by ADAMCH (004). Besides, i was esablished ha increase in he kinemaic cndiins he perain he cenriugal spreading l is limied by he srengh he granules he erilisers. Therere, when using he cmmn cnsrucin maerials and kinds erilisers, he pssibiliy increase he wrking widh he machines by increasing velciy is exhaused. In rde pimise he cenriugal spreading l wih an inclined axis rain, i is necessary have a mehdlgy which wuld ensure deerminain abslue velciy erilisers leaving is surace and he angle beween he vec he laer and he hriznal plane depending n he parameers and cndiins perain he cenriugal spreading l, as well as he physical and mechanical prperies mineral erilisers. I is knwn ha an increase in he disribuin widh mineral erilisers using he cenriugal spreading l is pssible by reaching rainal values angle, were described by ADAMCH (005). The bained resuls research winess ha he rainal values angle are siuaed wihin he limis 30 о 35 о. A he same ime i was esablished ha he exising cenriugal spreading ls can 109

2 reach he values angle n higher han 15.7, were described by ADAMCH (00). The cenriugal spreading ls wih an inclined axis rain ensure highepimal values angle, were described by ADAMCH (005). The amiliar mehdlgies by using which ne can deermine abslue velciy a eriliser paricle leaving he cenriugal spreading l wih a verical axis rain, were described by ADAMCH (010) and he mehdlgy which allws deerminain abslue velciy a eriliser paricle leaving he cenriugal spreading l wih a hriznal axis rain, were described MATERIALS AND METHODS The design he cenriugal spreading l develped by us wih an inclined axis rain cmprises a la disk which has blades radially insalled n is wrking surace and is cinemaically jined wih he drive uni rary mvemen. Besides, he axis rain he cenriugal spreading l is arranged a an angle he hriznal plane. Fr such a cenriugal disribu mineral erilisers we will build an esimaed mahemaical mdel he mvemen a maerial paricle alng is radially insalled blade s ha he axis rain he spreading l has an inclinain. Fr his purpse, irs all, we will cmpse an equivalen scheme in which we will shw he maerial paricle mving alng he blade he inclined spreading disk, and we will shw he rces acing upn i (Fig. 1). There: M he iniial psiin he eriliser paricle n he blade, pin S he curren psiin he eriliser paricle n he blade, pin О he cenre rain he cenriugal spreading l. Furher, simpliy he analyical sluin he presen ask, we make he llwing assumpins: he ceicien ricin he eriliser paricles agains he surace he blade has a cnsan value; he charace he mvemen each eriliser paricle is he same, and i crrespnds he characer he mvemen he enire mass erilisers alng he blade; he eriliser paricle is mving alng a secin he blade which is cmmn r he verical wall he blade and is bm, wihu a rlling min; he hickness he blade and he diamee he eriliser paricle are negleced. An essenial dierence dispersin he paricles mineral erilisers using he cenriugal spreading l wih an inclined axis rain, in cnras he hriznal ne, is ha here here are basic dierences by VASILENO (1960, 1996), BLGAOV (014) d n cnsider deerminain abslue velciy a eriliser paricle leaving he cenriugal spreading l wih an inclined axis rain he hriznal plane. The aim he invesigain is bain new analyical dependencies in rde discver he impac he design and kinemaic parameers and mdes perain an inclined cenriugal disribu mineral erilisers, paricularly, he value abslue velciy he eriliser paricles leaving he disribur disk, as well as heir accelerain angle. in he psiin vecrs rces applied he maerial paricle depending n a which place he inclined disk mineral erilisers are supplied and gripped by he blades: a he upper pa he inclined disk r is lwer par, a he righ side he axis rain r a is le side. This circumsance shuld als be cnsidered in analyical sluin he presen ask. a) b) Fig. 1. An equivalen scheme he mvemen a eriliser paricle alng he blade he spreading disk inclined a angle he hrizn (а, b respecively, a eriliser paricle is mving alng he blade wihin he limis secrs I, III and II, IV): 1 he disk; he blade; 3 a eriliser paricle 110

3 A irs le us wrie an equain in rde deermine abslue velciy a eriliser paricle leaving he cenriugal spreading l. I will be equal : V V V AC rc NC V rc, (1) where: relaive velciy he mvemen a eriliser paricle a he mmen i leaves he surace V NC he cenriugal spreading l m s -1 ; ransprain velciy he mvemen a eriliser paricle a he mmen i leaves he surace he cenriugal spreading l m s -1. V NC In his case he ransprain velciy he mvemen a eriliser paricle a he mmen i leaves he surace he cenriugal spreading l can be deermined by means such a dependency: V NC R, () where angular velciy he cenriugal spreading l, s -1 ; R he radius he cenriugal spreading l, m. In rde deermine, i is necessary, irs all, have a dependency r he esimain relaive ve- V rc lciy. Due he ac ha he prjecin he cmpnen rce P weigh he eriliser paricle upn segmen АВ in he prcess is mvemen alng he blade changes he direcin he vecr, i is purpseul divide he cenriugal spreading l in secrs in such a way ha he direcin he vecr in he prcess is mvemen did n change wihin he limis each secr. Fulilling his, we bain ur muually equal secrs: EOG I; GOC II; COD III; DOE IV (Fig. ). Segmens EC and DG are muually perpendicular diameers he la disk bu segmen EC rms angle wih he hriznal plane. Le us deermine he values rces acing upn he eriliser paricle M and wrie an equain r he F r resulan rce under he impac which his paricle will mve alng he blade (Fig. 1, ). Since he mvemen he maerial paricle he mineral eriliser prceeds in a recilinear direcin alng he surace he blade, we will wrie his equain in he rm prjecins upn he axis which cincides wih he surace he blade isel: Fr Fc P Fk Pn P n, (3) where: he ricin ceicien he eriliser paricle M agains he surace he blade. Le us deermine he values rces applied paricle M, which cnsiue expressin (3). The resulan rce under he impac which he eriliser paricle M is mving alng he blade is deined as: Fr m d, (4) where: m he mass he eriliser paricle, kg; L he pah cvered by he eriliser paricle mving alng he blade, m; he ime (durain) he mvemen he eriliser paricle alng he blade, s. Fig.. A scheme he disribuin he resulan rce under he impac which he eriliser paricle is mving alng he blade he cenriugal spreading l: а, b, c, d respecively, he eriliser paricle is mving alng he blade wihin he limis secrs IV, I, IIІ and II The cenriugal rce ineria is deermined by means he expressin: Fc mr, (5) where: r he disance rm he cenre rain he cenriugal spreading l bere he curren psiin he eriliser paricle n he blade, m; angular velciy he cenriugal spreading l, s -1. The prjecin he cmpnen rce P he weigh he eriliser paricle upn segmen АВ is deined as: P P cs, (6) where: he angle beween he cmpnen he rce weigh АВ, rad. P F c and is prjecin upn segmen 111

4 The cmpnen rce P he weigh he eriliser paricle acing alng he surace he disk, parallel segmen EС, will be deined by such an expressin: P Psin, (7) where: he angle beween he axis rain he cenriugal spreading l and he verical plane, rad. Frce P he weigh he eriliser paricle will be equal : P mg, (8) where: g he ree all accelerain, m s -. The Crilis rce ineria is deined by he expressin: Fk m d. (9) The cmpnen he rce he weigh he eriliser paricle acing alng he nrmal he bm he blade has such an appearance: Pn Pcs. (10) The prjecin he cmpnen rce he weigh he eriliser paricle upn he nrmal segmen АВ will be equal : Pn Psin. (11) I shuld be remarked ha in case he paricles (he lw) erilisers cme n he surace he cenriugal spreading l wihin he limis secr I r IV, hen in expressin (3) bere rce ne shuld pu he sign, i wihin he limis secr II r III, hen i is necessary pu he sign + bere he symbl his rce. By subsiuing he values rces deined by expressins (4) (11) in equain (3) we will bain a dierenial equain he mvemen he eriliser paricle M alng he blade he cenriugal spreading l, inclined a angle he hrizn: P P sin cs cs sin sin d m mr mg m mg mg d (1) As i llws rm Fig., depending n he secr in which erilisers are supplied n he surace he cenriugal spreading l, he values angle beween he cmpnen he vec he rce P weigh and is prjecin n segmen АВ will be dieren, and he values his angle are deined by such ur expressins: r he case when erilisers cme n he surace he cenriugal spreading l wihin he limis secr I, where: he angle rmed by segmens OE and OB a he cnac mmen he eriliser paricle wih he blade, rad; r he case when erilisers cme n he surace he cenriugal spreading l wihin he limis secr II, where: he angle rmed by segmens OG and OB a he cnac mmen he eriliser paricle wih he blade, rad; r he case when erilisers cme n he surace he cenriugal spreading l wihin he limis secr III, where: he angle rmed by segmens OC and OB a he cnac mmen he eriliser paricle wih he blade, rad; r he case when erilisers cme n he surace he cenriugal spreading l wihin he limis secr IV, where: he angle rmed by segmens OD and OB a he cnac mmen he eriliser paricle wih he blade, rad. Furher we will wrie an equain r disance r rm he cenre rain he cenriugal spreading l he curren psiin he eriliser paricle n he blade. I is deined by means he expressin: r r L, (13) where: he radius he supply he eriliser paricle n he cenriugal spreading l, m. By subsiuing in expressin (1) he value disance r and making a series ransrmains we will bain: S d L r sin cs cs sin sin L g g g d d. (14) 11

5 Le us cnsider a case when he erilisers are supplied n he surace he cenriugal spreading l wihin he limis secr II (GOC). Then equain (14) will have he appearance: d L L r g cs d d g sin sin g sin cs. (15) In such a way a linear dierenial equain he secnd rder is bained wih cnsan ceiciens and he righ-side par. Le us slve he bained dierenial equain (15). Is characerisic equain will lk like his: 0, (16) bu is rs will crrespndingly be equal: 1 1 1,. (17) Le us wrie a general sluin L equain (15) wihu he righ side: 1 L С1e Сe, (18) where: С and С 1 arbirary cnsans. Furher we will ind a speciic sluin equain (15). Le us inrduce he llwing designains: r g cs, gsin. (19) Then, aking in accun he acceped designains, he righ side he dierenial equain (15) will have such an appearance: (0) In his case we will lk r he speciic sluin he heergeneus equain in he llwing way: L W sin Z cs J (1) where: W, Z and J he unknwn ceiciens. These unknwn ceiciens are deined using he mehd indeinie ceiciens. Fr his, we will wice diereniae he speciic sluin (1). We have: Wcs Zsin d () Wsin Zcs d (3) Le us subsiue he bained expressins () and (3) in equain (15). We will have: L cs sin cs cs W sin Z W cs Z sin W sin Z J sin cs. (4) Perrming he necessary ransrmains expressin (4), we will bain: cs cs W sin Z W Z cs sin W sin Z J sin cs. (5) Furher we equae he ceiciens a he crrespnding rignmeric uncins. We have: W Z W, Z W Z, J, (6) W Z, Z W, J. r (7) Frm he bained sysem linear equains (7) in relain unknwns R, S and T we ind he values hese unknwn ceiciens: J W, Z 0,. (8) Subsiuing he values he bained ceiciens (8) in expressin (1), we bain a speciic sluin he heergeneus dierenial equain: L sin. (9) The general sluin he dierenial equain (15) can be wrien like his: 1 L L L С1e Сe sin. (30) The arbirary cnsans С1 and С are und rm he llwing iniial cndiins: 0 a 0 : L 0, d. 113

6 Fr his, we diereniae by expressin (30). We will have: 1 1C1 e Ce cs d (31) sing he presened iniial cndiins, we bain he llwing sysem algebraic equains in relain unknwns С and С 1 : С1 С sin 0, 1C1 C cs 0. (3) RESLTS AND DISCSSION In rde arrive a a inal sluin he dierenial equain (15) and esablish he rule he mvemen a eriliser paricle alng he blade he cenriugal spreading l, inclined a he hrizn (35), we subsiue he bained values (33) and (34) he arbirary cnsans С1 and С in expressin (30): L cs sin e cs sin sin sin e. (35) Aer subsiuin expressins (33) and (34) in expressin (31), we bain he rule abu he change V r velciy in relain he mvemen he eriliser paricle alng he blade a an arbirary mmen ime : V d cs sin r 1e cs sin sin e cs (36) In rde deermine he ime he mvemen a eriliser paricle alng he blade rm he pin is supply (pin M ) he pin is leaving he blade (pin B ), i is necessary replace L in expressin (35) by is value L R, which deermines he disance beween pins M and B, and slve he bained equain in relain ime 1 1 By slving he sysem equains (3) we ind he values he arbirary cnsans С1, С : cs sin С (33) And cs sin sin С (34). By subsiuing he bained value ime in equain (36), V rc we bain value he relaive velciy he mvemen he eriliser paricle a he mmen when i leaves he surace he spreading disk. In such a way, aking in accun expressin (1), we have a pssibiliy deermine he value abslue velciy a he mmen i leaves he surace he spreading disk, when erilisers are supplied n he surace he disk wihin he limis secr II (GOC). sing he bained analyical expressins, in accrdance wih he wrked u prgramme, numerical esimains were perrmed n he PC, which prvided a pssibiliy deermine he impac, and upn VAC. I has been esablished ha increase in he value rm 0 о 90 о leads he change n mre han by 0.1 m s -1. The impac and r upn VAC is presened in Fig. 3. As i is eviden rm he graphs in Fig. 3, a = s -1 increase rm 0.1 m 0.3 m leads a decrease rm 41.3 m s m s -1. Besides, increasing rm 6. s s -1 a = 0.1 m resuls in he increase rm m s m s -1. The chice he secr he supply erilisers n he spreading disk aecs bu lile he value VAC. Thus, a R = 0.34 m, = 0.55, 90 о, = 0. m, 1, = s -1 he values VAC will be he llwing: secr I = m s -1 ; secr II = m s -1 ; secr III = m s -1 ; secr IV = m s

7 = 0.55, 90, = 0. m, 1, ω = s -1 he a values will be: secr I β α ; secr II β α ; secr III β α ; secr IV β α 3. Fig. 3. Dependence abslue velciy a eriliser paricle leaving he surace he spreading disk n he radius is supply (erilisers are supplied n he surace he disk in secr II a R = 0.34 m, = 0.55, 30, 1 ):1 = s -1 ; = 78.5 s -1 ; 3 = 5.3 s -1 ; 4 = 6. s -1. In rde deermine he value he angle a which erilisers leave he spreading disk, a irs i is necessary ind u he place heir leaving. Cnsidering ha he psiin he blade a he mmen is cnac wih he eriliser paricle is knwn, i is expedien use angle is accelerain in rde deermine he place rm which erilisers leave he spreading disk. The angle accelerain is an angle beween he psiins he blade a he mmen is cnac wih he eriliser paricle and he same blade a he mmen when erilisers leave he disk. Le us wrie an equain deermine angle : a. (37) sing expressins (35), (36) and equain (37) he impac parameers, r and upn a was sudied. The bained resuls are presened in Fig. 4 and 5. On he basis he graphs in Fig. 4 ne can draw a cnclusin ha a high values he impac he inclinain angle a he axis rain he spreading disk upn he accelerain angle he eriliser paricle is insigniican. Thus, a = s -1 increasing rm 0 о 90 о resuls in a decreased values rm о о. I has been esablished ha increasing rm 0.1 m 0.3 m leads decreased values rm о a 3.4 о. Besides, he chice he secr he eriliser supply n he surace he disk aecs a lile he value angle a a a. Thus, a R = 0.34 m, Fig. 4. Dependence he accelerain angle a eriliser paricle n angle (erilisers are supplied n he surace he disk in secr II, a R = 0.34 m, = 0.55, = 0. m, 1 о ): 1 = s -1 ; = 6. s -1. Fig. 5. Dependence he accelerain angle a eriliser paricle n radius is supply n he disk (erilisers are supplied n he surace he disk in secr II, R = 0.34 m, = 0.55, ω = s -1, 30, 1 ). The use he revealed dependencies and he mehdlgy r he deerminain he angle a which he eriliser paricle leaves he surace he spreading disk prvides a pssibiliy bain iniial daa r he esimain he disribuin disance a eriliser paricle by he spreading disk. In is urn, deerminain he disribuin disance he eriliser paricle rm he cenriugal spreading l makes i pssible subsaniae her rainal parameers and mdes perain he cenriugal spreading l. a a 115

8 CONCLSIONS 1. New hereical dependencies have been revealed which describe he mvemen a paricle mineral erilisers alng he radially siuaed blade he cenriugal spreading l he axis rain which is arranged a an angle he hriznal plane.. The resuls numerical esimains n he basis he newly bained rmulae allw evaluae he degree impac individual parameers he inclined cenriugal spreading l r he disribuin erilisers by he value abslue velciy he paricle leaving he disk and bain iniial daa r he esimain he disribuin disance mineral erilisers. REFERENCES 1. BIOCCA, M. ET AL.: Aerdynamic prperies six rganmineral eriliser paricles. In: Jurnal Agriculural Engineering. N 44 (e83), 013: pp ADAMCH, V.: Impac he parameers and mdes perain he spreading l upn is leaving by he mineral eriliser paricles. In: Herald Agrarian Science. iev, N 1, 004: pp (In krainian). 3. ADAMCH, O.: Raising labur eiciency he machine r he disribuin mineral erilisers. In: Mechanisain and Elecriicain Agriculure Glevaha: IMESH, N, 005: pp (In krainian). 4. ADAMCH, V.: Subsaniain a mdel r he applicain mineral erilisers // Inerdeparmenal subjec cllecin. In: Mechanisain and Elecriicain Agriculure. Glevaha, IMESH, N, : pp (In krainian). 5. ADAMCH, V.: Thery cenriugal ls r he disribuin mineral erilisers. iev: Agrarian Science, 010: pp (In krainian). 6. VASILENO, P.: Thery he mvemen a paricle alng rugh suraces agriculural machines. iev: ASHN, 1960: 83 p. (In Russian). 7. VASILENO, P.: Inrducin in erramechanics. iev, Selhzbrazvaniye, 1996: 5 p. (In Russian). 8. BLGAOV, V. ET AL.: Thery min a maerial pin alng a plane curve wih a cnsan pressure and velciy. Agrnmy Research. Vl. 1. N 3, Esnian universiy Lie sciences. 014: pp Crrespnding auhr: Semjns Ivanvs, Lavia niversiy Agriculure, Lavia, semjns@apll.lv 116