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Bulle in UASMV Ag icul u e, 66 (1)/2009
P in ISSN 1843-5246; Elec onic ISSN 1843-5386
Cen i ugal Disc Sp eading Quali y as a Func ion o Feeding Posi ion:
Simula ions and Expe imen s
Ágnes GINDERT-KELE
1)
, E zsébe ANCZA
1)
, Zol án HAGYMÁSI
1)
1)
Uni e si y o Deb ecen Cen e o Ag icul u al Sciences and Enginee ing,
Böszö ményi s .138., Deb ecen, Hunga y; ba ane@ag .unideb.hu
Abs ac . A combina ion o an imp o ed analy ical model o he desc ip ion o pa icle
mo ion on he spinning disc and hodog aphic ballis ics in he ai was desc ibed ea lie . The uni ied
model (Ginde -Kele, 2006) is conside ed nea ly exac o single pa icles lea ing a conical disc wi h
pi ched s aigh anes. ”In-silico” sp eading calcula ions wi h expe imen ally cha ac e ized pa icle
clus e s a e sensi i e o bo h sp eade and e ilize p ope ies. Howe e , pa ame e s like loading a ea
and ai -d ag coe icien s may need empi ical co ec ions. In his wo k expe imen al and simula ed
sp eading pa e ns a e compa ed demons a ing he impo ance o he angle selec ion o e ilize
eeding.
Keywo ds: e ilize , spinning disc, sp eading, quali y
INTRODUCTION
Spinning disc cen i ugal e ilize sp eade s a e impo an since 90% o he 140
million ons/annum wo ldwide e ilize p oduc ion is sp ead using his simple and obus
ool. Modelling o sp eading is use ul because o he possible subs i u ion o expensi e indoo
expe imen s. A sp eade wi h wo spinning discs is implemen ed in he p esen calcula ions.
MATERIALS AND METHODS
The esea ch has been ca ied ou a he Depa men o Enginee ing, Cen e o
Ag icul u al Sciences Uni e si y o Deb ecen. In ou ea lie expe imen al s udies (Ginde -
Kele, 2003) we measu ed he indi idual ai esis ance ac o s k
ai
(Ho s ee 1992, G i 1997)
and masses m o 250 pa icles. Fe ilize NPK 15-15-15 (Ag olinz Ag ochemikalien GMBH)
was used, pa icle ic ion ac o on he ane µ
µµ
µ = 0.22, ane leng h l
ane
= 0.40 m, in e nal
adius o he disc
p
= 0.05 m (whe e he anes a e a ached). The cone angle o he disc was
Ω
ΩΩ
Ω = 9
o
, he disc o a ion equency n = 840 e /min, he ac o eloci y
= 8 km/h. The
dis ance be ween he wo discs is 0.9 m, and he disc e ical posi ion is 0.9 m. The co ec ion
ac o o expe imen al ai d ag coe icien s was co = 0.6. Cons an angula window o 50
o
o
he loading o i ice was used. Ha ing hese alues ixed, we sys ema ically changed he
loading posi ion on he disc (bo h expe imen ally and in he simula ions), ha was
cha ac e ized by he cen e angle o he loading o i ice wi h espec o he x axis
(pe pendicula o ac o mo emen ) and he adial cen e o he eeding place. In he
expe imen s he loading adius was in he 0.1 - 0.14 m ange, while he cen al angle was
changed be ween -39
o
- 65
o
. The expe imen al alues we e iden ical wi h hose used as inpu
o simula ions. Fo hi een di e en loading a eas we ha e expe imen al and calcula ed
esul s, ha a e compa ed and analyzed. Expe imen al sp eading pa e ns we e ob ained om
ou doo sp eading es s using he weigh s o he collec ed bins ha we e u he ex apola ed
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wi h calcula ions o de i e he sp ead pa e ns. All calcula ions we e ca ied ou wi h he
MATLAB p og am package.
Fig. 1 Scheme o spinning disc ha shows wo o a ed posi ions o he disc.
RESULTS AND DISCUSSIONS
Below we show he esul s o calcula ed sp eading pa e ns wi h a “ i ual sp eade ”
ha has closely ela ed pa ame e s o ou es sp eade . Calcula ions o pa icle sliding on he
ane a e ex emely as , since analy ical o mulas a e used (Din wa 2004). The calcula ed
discha ge eloci y dis ibu ion is shown o he lea ing pa icles. On he same igu es he load
angles and he mean o discha ging di ec ions is also shown. These a e he inpu s o he
ballis ic calcula ions (Ká mán 1967) ha yield he landing posi ions o each pa icle on he
soil. Fo simplici y, he landing posi ions o he second disc a e ob ained as mi o images o
he i s disc.
Repea ed calcula ions wi h inc emen ed swa h wid hes gi e he mos impo an
cha ac e is ics o a sp eade : he sp eading quali y (CV %) as a unc ion o swa h wid h.
These calcula ions we e accomplished in wo ways. The adi ional e e ence o he
calcula ion o CV is equal wi h he pe inen swa h wid h. Since in his case he e e ence
bandwid h is educed simul aneously wi h swa h wid h, he quali y o sp eading will no be
“spoiled” a small swa h wid h. T adi ional calcula ion also supposes a numbe o ac o u ns
on la ge a able lands. In ou al e na i e app oach only h ee ac o u ns a e conside ed in a
“ ace ack” sequence ha p edic s less uni o m sp eading a small swa h wid h. The me hod
p esen ed he e uses a cons an e e ence bandwid h calcula ed om he di e ence o maximal
and minimal cas ing dis ance. This kind o CV de ini ion may be p e e ed o si e speci ic
applica ions, whe e only a ini e numbe o ac o u ns a e necessa y. Analyzing he esul s
acco ding o he new CV de ini ion he numbe o use ul swa h wid hs can be p edic ed
( hose, ha p oduce CV < 15%). Fo be e compa ison, he adi ional way o CV
de e mina ion is also applied and shown. The o e all quali y o he sp eading can be
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calcula ed as a a io o he a ea bo de ed by he pe inen CV cu e and he limi ing 15% CV
line and e e enced o he possible bigges 100% a ea (all ze o CV) o he ‘expe imen s’. Fig.
2. shows a sligh ly skewed discha ge eloci y dis ibu ion, ha can be compensa ed by he
impac o he second disc.
Fig. 2. Dis ibu ion o he eloci ies o discha ging pa icles ( eeding a -53
o
and 0.12m adius)
Fig. 3. Calcula ed CV% a iances as a unc ion o
swa h wi h ( eeding a -53
o
and 0.12m adius) Fig. 4. Expe imen al CV% a iances as a unc ion o
swa h wi h ( eeding a -53
o
and 0.12m adius)
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S udying Fig. 3 and Fig. 4 we can compa e he expe imen s and simula ions o he
gi en se ing o he eeding o i ice (-53
o
). The ag eemen looks sa is ac o y, hough we ha e
o emembe ha he ai d ag co icien s a e empi ically co ec ed in he calcula ions. Fo
comple eness, Fig. 5 shows he expe imen al ans e sal sp ead pa e n ha is he inpu o he
gene a ion o he p e ious Fig. 4. Fig. 6 wi h a sligh ly miss se eed angle (-48
o
)
demons a es ha CV cu es a e a he sensi i e o hese pa ame e s.
Fig. 5. Expe imen al ans e sal sp eading pa e n om he masses collec ed om he bins ( eeding a -53
o
and
0.12m adius).
Fig. 6. Calcula ed CV% a iances as a unc ion o swa h wi h ( eeding a -48
o
and 0.12m adius).
This se ing o he eeding o i ice spoils he quali y o sp eading.
The esul s o all hi een calcula ions a e shown in Fig. 7, and i can be concluded,
ha he mos uni o m and obus sp eading is expec ed in he - 65
o
- 55
o
eeding angle ange.
A alues lowe han -50
o
, he sp eading pa e ns become much wo se, due o he pa en
ans e sal pa e ns, ha exhibi wo maxima.
Analyzing hi een “ i ual” expe imen s wi h he pa ame e s o he eal ones, he
dependence o quali y and obus ness is shown as a unc ion o he eed angle (Fig. 7). I can
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be seen ha hese p ope ies ab up ly dec ease below -50
o
. Consequen ly, sp eading wi such
se ings is no ecommended.
Fig. 7. Analysis o hi een simula ions shows ha he quali y and obus ness o sp eading b eaks down a eed
angles below -50
o
.
CONCLUSIONS
I has been shown expe imen ally and by calcula ions ha he quali y and obus ness
o sp eading o cen i ugal sp eade s is e y sensi i e o he se ing o he loading o i ice
angle. The e o e a ca e ul adjus men may be c i ical in e e yday p ac ice.
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