M
Processing and p An Introduction
A. Gupta and D.S. Van
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ISBN·13. 97l!--1).4-I4-S1636-7 ISBN·IO; 1). 44 ~ - ~ 16J6..0
For info.m.l1iOll on 011 EIK'i« rOOiiOlltiono ,;'" out "'
Printed ..,d bound in Tho N<1h<'londs 0607080910
1098765~J21
TO
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CONTENTS CHAPTER 1. MINERAL SAMPLING
I. n-mtODUCTlON l.l. STATISTICAL TERMINOLOGY
1.2. MINERAL PARTlCLliS DU'FERlNG IN SIZE - GY'S METHOD 1.3. MINERAL PARTICLES OF DIFfERENT DENSITY I.~ . INCRE.'lEl'oTAL SAMPLII'G U. OOm1NUOUS SAMPLING OF STREA.\lS 1.6. SAMPLING ORES Ot· PRECIOUS METALS 1.7. SAMI'I.INO NOMOQRAPHS 1.8. PROBU'.M.S REFEREKCES
\ \ 7 II 13
20 24 25 28 31
CHAPTER 2 PARTICLE SIZEESTlMATION AND DlSJlUBUllOSS
2.
n-mtODUcnO~
2.1. METHODS OF SIZ£ ESTIMATlO~ 2.2. PARTICLE SIZE DlSllUBUTION 2.3. COMSINING S17J! DlSTRlSUT10NS 2-4. PROBLEMS REFEIlID'CES
)2
n 45 53 59 62
CHAPTER 3. SIZE REDUCTION AND !!NERGY REQUlREMIlNT 3. NrRODUCTION 3.1. DESIGN Of SIZE REDUCTION PROCESSES l.2. EI'o'ERGY FOR SIZE REDUCTIO:'; • WORK INDEX 3.1. ESTIMATION OF WORK INDEX I'OR CRUSHERS AND GRINDING MILLS 3.4. PROBU'.M.S REfERENCES
63
63 65
lit 92 'YI
CHAPTER 4. JAW CRUSHER 4 . NrRODUCTIOS 4.1. 42. 4.3. 4.4.
DESIGN Of JAW CRUSHERS JAWCRUSI1EROPERATlON JAWCRUSHERCAPACJTY CRJTICAL OPERATIND SPEED 4.5. POWER CONSUMPTION 4.6. PROBLEMS REt'ERE/
~ ~
,m ,~
". '" '"m
CHAPTER 5. GYRATORY AND CONE CRUSHER
S. lNTlI.ODUCTION S.1. DESIG~OFGYRATORYCR US HERS S.2. GYRATORY CRUSHER CIRCUIT DESIGN
'" m '"
, B. GYRATORY CRUSHER Dr[RATION ~ . 4 , CAPACITY
'"'"
'"no
5.5. POWEll. CONSU:vJI'TION PROBUiMS REf ERENCES
~.6,
'"
CHAPTER 6. ROLL CRUSHERS 6. IN1RODUCnON
'" ,,'" '" '" '" '" '"
..
6.1 . DESIGN OF ROll CRUSHERS 6.2. OPERAnON OF ROLL CRUSHERS 6.3. OJ'AC/TY OF ROLL CRUSHERS 6.4. POWER CONSUMPTION OF ROLL CRUSHERS 6.S. HIGH PRFSSURE GRINDING ROLLS (HPGR) M . OPJORA'llQ:>I O~ ItI'(jR
,~
6,7. CAPACITYOfHPQR 6.1. POWER CONSUMPTION Of HPGR
M . PROI;lLEMS
'"
REFERENCES
CHAPTER 7. nmUlAR BAll. MILts
7. u.,.IRODUCTION
'"
.
,'"
7.1, DESIGN OF TIlBUlAR MILLS 7.2. OPERAnON OF TIJBULAR IIALL MILLS
,~
7.3 . ESTIMATION OF MILL CAPACITY 7.4. MILL POWER DRAW-MEClIA)
'"
7.S. PROBLEMS
W.
REFERENCES
"" '" '" '" '" '"
CHAPTI:.R I. TIJBlJU.R ROD MlLl.S
B. INIlI.ODUCTION 1.1. DESIGN OF ROD MILLS
8.2. OPEI!.A TlON m' ROD MILLS B.) , ROD MILLCAPJl.C!TY U. ROD MILL POWER DRAIT
= m
8.5. MILL DRIVE 8.6. PROBl.F.MS REFERENCES CHA I"ffiR 9. AlITOGENOUS AND SKI.f!·AlITOOFNOUS
MIU .~
9. INTRODUCTION 9.1. DESIGN OF AG/SAG MILLS
9.2. OPERATION OF AG/SAO MILLS 9.). AG/SAG MIl l POW£;.R 9..4. CHOICE OF omONS BETWEEN AO A,,"O SAG MILLS 9.' . PROBLE.\!S
JUlFERENCES
'" '" no '"
,'". m '"
" CHA mR 10. )'lAltIEMAllCAL MOOOUJNG 1:-: COMMI~unON
10. INTRODUCTION
255
10.1, BASIS FOR MODELLING COMMl)'.' UTlON S YS'I'E MS
256
10.2. MAlllEMATrCAL MODEI-S or CO~IMlNlITION PROCESSrs 10.3. MODELLNGCkUSlliNOANDGlUNDINGSYSTEMS 10.4, PROBLEMS REFERENCES
26) 268 288 29 1
CIiAI'TER 11. SCREENING 11. INil!ODCCTION
11.1 . RASle DESIGN FEATURES IN SCREENS
11.2 OPERATION OF STRAIGHT SCREEN S 11.3. CAl'AClry ANIl SCREEN SELECIION U ~' STRAIGHT SCREENS 11.4. OPERATION OF CURVED SCREENS 11.5. MODELUNG OFTHESCREEl\"NG PROCESS
11.6. SCREENfl'.:G AND CRUSlliNG CI RCUITS 1 U . PROBLEJ.1S REFERD:CE-~
ClIAPHR 12. CLASSIFICATION
12. lNll!.ODUCTION
12.1. OESIGN f L\ TIJRES OF ).tECI1AN1CAL CLASS IFI ERS 12.2. OF-S1GNING 'fIlE POOL AREA OF MECHANICAL CLASSIFIERS 12-3. DI;..~I(]r<: FEATURES OF CEl'-'TRIFUGAL CLASSIFIERS 12.4. OPERATION OF MECIIANICAL CL\SSIl'I~RS 12 . ~ . CAPACITY OF MECIlM'ICAl. CLASSIFll,RS 12.6. OPERATION OF CENTRIFUGAL CLASSIFIERS 12.1.IIYIJROCYCWNE MODELS 12.8. IlYDROCYCtQNECAPAClTY 12.9. IIYDROCYCtQt->E CIRClJlTS 12.10. PROBLEMS REFERENCES CHArrER
n.
'" '"' 293
'" 'm"
".".
'" l~ 3~ 4
359 ]<,5 369 377 378 386 388 392 39~
399
SOLJD-Ll()U1D~EPARATION
13. IN"il!.O DUCTION 0.1. Df~IG:-: FEATURES OF THICKENERS 13.2. THICKENER IJESIGJ'-BATCH PROCESS 13.3. THICKENER DESIO)<," ·COi'ITJ'-IIJOIJS Til fC KENERS 13.4. OPI,RAT ION OF THICKENERS 13.5. TIlICKENERS IN CIRCUITS 1).6. PROIJLE).1S REFERESCES
~, ~,
~ ~
'" '" '" ".
,; ;
CHAPTER 14. SOLID L1QUIDSEPARATION· FILTRATION 14. INTRODUCTION DES1GS FEATURES OF Ft LTERS OPERA nON OHIL TERS Ci\PACITY OF CO:-nJNUOUS VACUUM FILTERS WASHING OF DEPOSITED CAKE DRYING OF OEPOSITEDCAKE opn~f UM THIC KNESS Of CAKE FIt TERlNG MEDlA 148. FllTERlNGAIDS 14.9. FIlTRATIO~ IN ~nNERAL PROCESSING CIRCUITS 14 .10. PROBLEMS REFERENCES 14. 1. IU . 10 . IH . 14 S. 14.6. 14 .1.
". ". '" m ""
...'" ... .~
m m
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CHAPTER IS. GRAVITY SEPARATION
IS. INTRODUCTION
.~
IS. I. PARnCLEst::rTllNGRATES
.%
15.2. GRAVITY SEPARATION OP~RAno,..;s 15.1. JIGS 15 4 DlFFERE~'T IAl MOTIO"'; TABLE SEPARATORS lS.S . FLOWING FILM COSCEJ<.'TRATORS 15 .6. DENSE(OR HEAVY) MEDIA SEPARATION 15.1. GRA VfTY SEPAKA nON PERFORMANCE l H . PROBLHfS REFERE."ICES
~,
m '"' '" m '" ,,. ~.
CHAPTER 16. FLOTATION 16.
INTRODUCTlO~
16.1. FLOTAnONREAGE/llTS 16 2. FLOTATION EQUIPMENT 16.3. FLOTATION CIRCUITS 16.4. FLOTAnON KINHICS 16S. FACTORS AffECTI NG THE RATE OF FLOTATIO:-l 16.1. OTHER FLOTATION ~ODIiLS 16.8 PROBLEMS REFERE.\lCES
m m
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.
,~
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CHAPTER 11. METALLURGICAL PROC ESS ASSESSMENT 11. INTRODUCTION 17.1. 11.2. 17.J. 17.4. lB.
Al'ALYSESorCONSTlTtiEJHS OI,"flNlTlON OF TERMS MATERIAL BALANCE CIRCULATING LOAD PROBLEMS
REFERE~C E S
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d ' - -,d '
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- diamclc"t of uphm: of "luoi w>lumc: - diamc:'cr ofo >pi .. ,e of "luoi • ..ru.c.: >=1 The values oflog r(F" I['FA V') Re" r and log r(F"'p.-A V,')Re' r cor=pooding to dirm-: "aI ..... ofs/>apc facwr. k. .... 1Ii"en in Table 1.3, To use !h.i.lllble.1og [(h /p,AV,) Re"1 is colculated fiom 0 .,...ured .. '~i"ll ' ·elocily. V r. "'i"ll Eq. (2,2 1) fo< a Oplocri<.ol particle and tho "lui,-a!"" Re val ... fOOM from Tablc 2,2. 'Ihe correc1ion valut from Tollle 1.3 i. lhrn appliCun< f"" tho "",>-~I shape of ,be "",,;';Ie. Tho: partido ,ize can tot cal
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panicle •. Tho:
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- 2078.64
Or V'
Then from Tobl< 2.1. log Re - 1.7143 or R< - S 1.7'1
Fmm rabl. 2.3 tho OOI'fehope fae'", of O,J ~LI3.1, • Q.00I47.
That is. lIle OOfT<">.W ,111 .. of u,li%
k'Il
~.
ro. ,he IlOf'>.Sp(!eric.l
p41\icle - 1.11 , 3 -
Q,()4.:7 -
and Re - 46.]3
Usually gravity segrq;a1ion method.
or<:
!!Sed to dc!onnioc: panicle oi"". Gown to 0.02
",'crons.
1.1.4. &Ji"''''/ali< """ of phcrial panick. ~' in~ S",... , ' La .... Ill< motion of the partidc in the «n' riful!<
rod,,,,
(2.14)
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"
Particle Size (microns)
DUtrihlltHm 10 some OU<:I! ,,11= Ihc distributiQn i, . - . • ~ .... plot .,.., be obtained b\" plO!tina !he lot of!bt CUDluloliVl: lIDil<:n;iu agoinst .... lot of lhe ......., "1'<"'=. prwn .. Gowdin-Schub:nan. pIo:s. 10 moot cues 1Iti, "",,"d yirld. IItnlipi line. n,.,..montage of JudI plOIS is 1hat. lirni!a bttwettl on)' lwe .i.... II 01"" ind"'-> .... diolribution of Ii.... ofpatticles !hal rolll in • sample. It is .... """'nary '" pi", both \he cumulative oversi .. and \l!ldenizc: as eaclI is lbt mirror ~oflh
GaNdin&~
,i..,..
r-100(:r wber<
(2.30)
Y
- oumulalive ...... OK p
•
-
k •
""""'" ~ oj"" _ . .... p.rome\er _ di~buti"" poromt\ef
Toki"ll !bt lop ofbodl >ideo of !hit eqIIIIioo and ~ I~ !be:D:
loKy - lotIl00 " .\o&x" . lojk or Io&y - .1oa' " COSSTANT
(l.ll)
1bi. i. !be eqUllion of. waiplline if. ODd Yon: ploltcd OIl ol<>g.&r... on
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" gi"'.
" plot of k>a 1"11 (lIl0/R) ",,'sus k>g, should strai~t Ii... The pararn«= "r the Kosi n_Komm:" dinnbuu"". b and x' .." obIair>Oi. speci.11I1'IfI/l paper i. ",-ail;obl< (R""',o.-l('onn'l<.-. ,-al"", u( ,wn ..... '" '4 ","",'f1P>< p>/ameter x', 111< m<\1>0<1 of ''''''PU,inl! f", • Rosin_R""'ml", plot is ill",,,,,l
,-.l""
Enmpk l .4 A ";"ve anaIp i ...'.owed the (0110,,'0& ... ull> (Table 2.6). PI", the daIa acoordin~ to a.udin" Sehunm...., and Rosin·Rommlcr and the ","", of Ih< liz< 1I1><' ion rn.oiocd on 200
dct""",,,,,
~
f ig. 2.11 i. a pi'" of tho <"","Ial;'-o
~.
passing <"luron in Tabl. 2.6 ,-""" •• j:illJl! Ii... thai ~-. \he fB<:hon of Min~ a 200 I"" sic,," was OXpe
Kosin-lUmmi., plot. <"" ,imHarly bo modo oithor by calculation,
Q'
u,ing 'I""io] 1<>1\
raJ'<' ~"""n a< Weil>ull gtaph p.tpkul..""".
T)l'ieal calculO!ioos usina the data in Tobie 2.6 is illustrated in Tobie 2.7. Thi s O< plot i. ""arty 0 . lraiKht lio<:. "hi<~ ioo;.,o".. "'"' lho m... ["",ti"" main«! on 200 rruorum is oboot '1(1.6 % by mass or 9.4 % pa~.
"• •• •• • •
,,,
••
, •• < •
!; •• ~
U
•
-. MM,
•
•• •• , •• ••
"
'00
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»
,
II
i---~·, · _1:2110.1>:
I
--- . .
,
~:;·.=='I ~- -
•• I ,I
,, , II
!J t
I
Ii
i !l,
I
.!, N
~".""":i
10.
, I)
!,,::::;"'-
," ••
.. ," ... ••
.. - .......
.;;'!!~
_:l'.,
:11> • •
j • • -. .i":"
.
I
;;!il~
J
N
i.I
::;~=:::::
fEi;~;;;=;=!~~~
- ... -....
i II
~!~:lln
" ;;;;;i :1Ii.!:!
..,,
~
i
... !!".:;,., =....~~ ' I dl:
••
,. •
.1
II . --- .... i $=, ~' ~::
, I
•"
". •
!I ,
••
I
:,;•
I
-... . ... ..
!!".
~=;~lt
•
h
"~=11111
•
i.IJ
,,"I ...
='1I~.
.... .,-..---..
;- ..~ ." ~~ ~::: =
••
•
H
-~
..
I
',' •
e,
,I .r t.... n"... -'" ..... ., - ..
--- •... j
.,
!
... - , ,
-".'''. --; ~~!:: .
";",~~,,
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Table 2.9 C"",~i"" cf cyd .... i' ....
P.,>i"ll ( microo 9.
S""
factor. 11 - 0.636
~~
Cwo % PaMing
Conwn,:d Size. (micruns)
(mi<:rotu)
N,
117.9
.,"
"" "" "•
"" '""
m.'
S96
499 337 230
S] .4 377 2S, I
lU
1&.9
l.4. P..,bkm.
"
0. .. obtainal
onaly;ing' IWIlbJing mill producl i.
~i",,",
below. PI", the data using the
Goudin-Schumann and Ro,in-RammJer melhod .. hom ,he ploU ""'imok ..... m... [""'lions r<:1IIin
feed. mass % .... ioed
"
U.in~ "'" follo"'inj:
nuss
1200 LS
300 10.0
600 ~ .o
ISO 22.0
.. ""
75
no
_7S 29,S
TOIaI ]00.0
da1.a. plot • Ro>in_Rammlcr di>lrib
8SO 125
2-3 Sample> .,r!be foed 10 • boll mill .... the
ond the: ,.,..,1" ""' OS r.,uo",'",
15.S
19,0
,W 16.0
'"
13.0
.,. 10.5
,~,
100,0
prod"", aile< IS min> of _rat"", ,,"'" ....ly....t
&lima,. the rate cf rtductioo cftbe 1000 '"'" feed size duil\i the mill ~ioo.
"
Th" prod"", from • ifir.dinj: miU ""' ..... rI ~ ""r=ro;d I01d onol)..... yielding ..... follo..-illg ,i.., di"";."."ion:
"''''''II''
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Chapte r 3. Size Redu cti on a nd Ene rgy Requ irement 3. I.YfRODUCT ION
In n.tu .... tnir.eral' exist in 1lh)"Si«J and chemical eombinalioru "'ill> each OIher. To....,....te min. To """" .. the: ~. in tho 00>1 rod.",. they ho,·. to be crushed aDd e"dl ~unetltl of ino=.. i, by oomminution from thc: par051 ro"<-r >um eidll quantities of \he useful mincnI 10 """'. til< OperatiOD CO!lIlIl<-r
be""..,. '"
....,....,«1
"It:
J . I, lln ll G of Slu R«Iuollon p, "..".. The pt'QQtl& of oi", .-..:II>hed in .be """" UlIi • .. seen b Fill. 3.2 . In.., doing tho load WI tho equipm'eraJ options in .. media c. ,code within & mill ond impinge on tho "'" thOil pro"idi",. ide • KrilKiini ""ion and fore .. of onrilion. oU
'!ai'
II""".
"'_ups,
....,.....«1
no...
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lbe >a.iuc of W. C&Il be oonsidertd to be ilIdepenoaip!S der>o!illll the *"~ oi.ze of feed find prodUO! ' ..pt
* R.... one!
dime:nJionI~ .., .. \Jie .......bet 10 ,",,~"i1U ~IOO mic:roru.
By defonitioo!be opeci& jlrindinl eneraY il!he """'lP' ""Iuirtd per w>i! IlWII oflht rod<. The opcciGo arlndina ......1I)' of I ~ar minmol il wriuen ""
(loS)
NOTE:
I. 2
kWMIl600 - JoWcoil. While 80% _illll • pooni<:uJar sieve is _oed .. IIUdard fur de!<;rmioillll !be W
_.un
In Bond·, equation. (Eq. (3.3)). the griroding eneri)'. Eo. ""Iuinod for Ii.. rcdu=!ion arrod,. in ;odllAiol mmbli"ll mills WII baed 011 mill Wft P"""'", Pw, ond Oft mill """";!y (Q) The .. lation>hip ~ ""10:
_ 'M. Q
(3.6)
For..,y rook ...... r""' !be ......C ""Iuind for romminutioD may be d of n (loS) in equation 3.1 shonId be tq>I.....! by (!+[WD. Thio equ&Iioo "",",,0 IC !be Boo:w:l equ&
(H) wbiclI ift effa:t is Iht Bond equatiOIL Bood". oriainol milk on eJ\Iblishing the
"""II)' for oi......oction wa es\Obli!hed in I 2.44
m (I foot) irolenlal di .......... "'"' ¥rindin3 uv..oow type boll mill. Dwb< i, III>W exp,n.d _ ! b e derived empirical equati"" i. applicable IC hiah I>esou .. roller c:ruMcrs "bore one: otagc opwsky """ Lin [tSl indiCOlions ..... thai !he: Rininll"" exP" "·M,1l - )( (lIP -1 1F~ is mote opplioabl. for IIize teduotion by high JI"OSS"'" rolls.
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" Alkr the o ."'~ from it. pooitiQa orm(. \hi: ,'.Iocity of the , . , _ pendulum woWd
pcoduhmt ~,
(3.1~)
where
II. ••'
- IheVMicaJboight.no.inedbytheblockpendulLll'll....! - Ibt velocity of"'" I>I<>ok Of tebotu>d pendolom oftet ;mp.cl.
oro;Ilbe o:orTeSpOnding energy ofreb:Jund will boo (3.16)
After the impecl, the vclocity orllle suikina pendulum dca 5" and V, ' MW will be jlive:o 7
'"•
• (v.' - v.' .l
Vs - vo - -.
WO-
(l .l?)
•
• vo'
v,'
- the velocity or .... bIod bd"", impo"'1*1
AI II>< initiol velQcity of tbe rrl>o>und bIo
:we. lPPlyioll NewI<>ol'. J..&w of
, ,
• • (V, _ V,)
"
(l.II)
•
Tho CIlCIJIY for crushin& Eo" tbe diITcren«: tid",=, "'" cDa'f.l' "r tbe input ptnduIwn and !be tiKi" oflhe ",bound pendulLlm ond is COIDpIII
Uniu: E'.nerirtemu(ll) - k\\'h/t - l6OOkJlt M...
_ 1<3
n..,1lIuecf. - 0 - 0.2 Tho n:ouIts obIaintd "jib the \arjeI' ..,"';1 blocl: ba.... been fouod 10 agree Vltll ""Ill Ibt ttlCr8Y C<>nSu/'IICd ill AUMS o"'II< and Semj.AIII<>QtMW Grit>iina (SAG) mills. while n:sulu from the omaIlcr onvil ~ more ..ith ball IIn
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(l.B)
~ to the iJindilli ,ircuit and the product P.
i. the: ,in:ui, this i. straightforward bu! in • c100ed cif"Olli, mill. where. classlfier;' irulallod '0 return the <:OW>< fraction to the mill, !he work i!>de>: i. b;>oed "" .... work dono in rmucina:!he size of the . "" ... fcod··, that i1. th< oriSinai f..d plu. the coane frx ' ion from tho product "'i>""'Lod at the cl4Mifier and mumtd to the mill fcod. n.. oprnt' ing ,,,,rk ioo.. i. uord for:
In .... Bond «I ..... io ....... fO«! F is the prodoct fiom the: i!indina citt"'t. In on
opal
L
Recordina: mill perfunnancc OIl • ",KUI..- twi. (b<>url),. Gaily etc.)
2,
Con'"",it\i cumnt pcrfonnancc with historical d.1I
J.
Comrorinl! cir<:uit:! in multi-cir<:u.i, plall"
Si""" the optnti"ll worl ioo.. i""lud.. motor, dri,'. and i!irx:lin& incffici""ies. it i. 001 dire.tory irindability work index .... c"" be ttsod ... tneaS\Il'e of grir>ding dlicimcy in .... pi""". (J.24)
w~
Woo:
~ op
i!>de>:. oolT<"C1od
ro.
IlOO·JIoIHIord condition. and """.
optimum fetd,
w, ttn
-
I.bor:>.tory i!indobility w"rk index,
r."
J.J.J 8mod Rt>d ,1/;1/ Stondm"d Standard conditions for d; ,iQn!l ~.
M ill Si..
_ J05 mm (inlemal diamelcr) • 610 mm (internal k nljlb) with _ '.. type lini"ll
M.. terial
Dry mir.eral 5i.. _ redocedtoIOO %< IJ2001"" Quantity _ 1250 em ' (tlIpp«! clown to ii~. ",producible bulk d ..... iW) (; . 38 ,1 mm di • • 0.53 m loni ,,..,1 f"O
Mill Rota,i"" _ 46 =Imil\. 100 % circul.Uina klad.
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7. Corncti(}ftfociur: F7 Mill ~ The arindina .fficitoe}' chanaes";!h mill diameter. The change ...... from the eIwlgc iD po ..... dro""" by tho mill ond tho tl\ang< u mill _ i l f with wOll>
n__
( '~)" o
F7 - 0.914
f... D < l .l lm
for D
~
HI m
(3J2)
the m,U d~> D, i. in .......... 11 .... b
"- C""",,,ioIofoctor FI! Rod ),.fim~ The oor=:tion _ for rod millina i:I complex ODd oIcpcod. 011 tho feed JAcpwlllioo:o. IIond auggestJ twI) conditions;
1.
2.
.'", .. rod mill only applkotion, .... on lOge only. If Ill< rod mill f=;[ i:I JO% ~ 12 mm or ..,.. (<0.11- from • d~ cifoJil
WOMaint~ in this correo:tiorl f..,tor f'O'n.!Ioa1 illla li1ll. val ... iD calouJotina. Wee \be .lfocienc~ of,.om rod mill pe
The
....
and by tbt prod.." of1he oOIl«:li"" factoro will fJi'
"""*- index
(3.33)
he",," r", ..,...!ilion not applicable obouId be tak ... .. I. The Bond W",t Index ,'Ill... c/wop with the si ..... oize ~ dllring .. porUculor __ For """,,,pie. in_d of ~ the oo:r<>eZI ~ tlirouBb wbich &0% of the "'" P" = , u.. """I size 1htou&h ",hich 15% "fthe ore p" .... may be ch<>oen '" oW, I por\iculII' condition ofmill opemiOll. Bond', ""&ina! upteS$kon [or u.. work iodu i. _ IlII BO% o[ the onaterW PUS;"lI • """"'" ,i.., Thi. hos b
""w
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oo· ... i'" i. n>:Ordod. TIll. "...... lo.d of2~0%.
10,
Moo
IIIK>uld be equal to tho nru,
Me at a eirt:u1atilli
The oo'iz< 1¢nJl"i rot. COO>Stall~ k. i5<.kuIo1«1 """iii tho
k • n(ln M, _lnM.,.)
(l,J7)
N - number of mill ,....'ol"Ii""" pet minute - nurnbdina
)..t., I I.
-
Ina.. ofto't
..,rmt ,w"";zo at the beiiMi"i of tho pil>dins toot
The toW number of mill ,....·olulioN f'" :he: KI>Ci ilil>dina test (N,) i. clicW.,,,, from 11>0 equati",,:
N
,
,
0 .38)
12. 13 .
The mill i, loaded with the occond c!wgo and irirw:l for N, .. >oIuli"",, Aft .. (Pindillj!. tho rntu. mill charge ;, ",rerncII tho test "'''''''' and the oo.... izc ond und<:nizc weighed, The o,'em..: IIhouId be oppro. imatdy equal to (2.SMI3.S) and It" maD of the unders.i ••• M",. should be "W"xima1
14.
The . i...... IY'i. of the 1<01 OCreeJl undersize i. deocnnine and the 80% "",",ina oitt
I S,
The ne", w>denizc per mill ",,·olution. G. in the oec«od a:rind ;. Ibm determined tho equation:
(PIO) of the prod"" calculaled,
u
,
M. __ M(I_m, ) G. 16.
3.5
(3.39)
N,
The ore WorI< Inde. i. then calcul .. '" ",illi the &nd formula (Eq.
J.ll ~
Thi. rne< the Mqd>.linm·ic method ""'. lhe!lllme [..ro to """~ ilindin~ step.. thi, biordor material in .... e;n:wati"i l<>ad i, "'" ,imulated and th<
""",i.,,,,,
metbod "'ill ii'·.' 10"'" WorI: Index ,-al.,..
,-..1""
he"".
1. M ..J,,"'~ lUl"I • ~OIt-. _d.n ,.iU.otd <•• ,,~ If. 0Iandard Bond mill i. "'" ..-allable then an approxirnat< Wor\;: lodex val"" can be obIoined if . sample of ore of known Won; Indo. i. .vaHable 1281. The mill
""".,tandar
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1bo """"loIion bl favtHlrS oIn.!ion t)']>< !nab&< ~'.. n thI" 1<"';1< ' 1I'milh ;. a fair indi""tion oflhc: . _iv...... of a rock. Briggs .."" meorurcl Ihc: brc:aUgc rat< and bmlbge dimibulion func tion of .... 0"" and ~ k' ic '"'" wilh "i~r rock! "vin~ , lower b«-""'i< nI1< . How,,'u Ihc: data !eI for _ tesb was mml and further ,,'0<1< need. to be don< to """finn tho ...la!ionship, Bearman eI ,I (3 81 .... asurtd . "i w... that Ihi. t«hoi""" "ill .... bl..... do", required for comminution pi.".
""'naIh
_=
1. n."."'I"II'~ SI.,iAlk..J M",~t>rI; index .. ini Ihc: Rosin-R.amrnler ond Oo..Jin-Sknown rock matOst oct bet..-..." 13s() ond n micro", and Ihc: R<>si,..Ramml.. di,nibulion 1"1""'..... ; is \hen calculoted from .be ....ti"iC2l PO"-'" ... IIlIion:
"l.n
(3.45)
",-bore x, is .... size ~. Xl. of .... R<>s;"'Rommler oqllMiOll of 3327 mitrib!Jtion of the same: f< 00",,-",,", a. ~. ~. d, < ondf""'''' found to Ita,... be
values of: a - B &t 73361 &, b - 0.003845. ~ - -14,81&65321. d - ~. 16S6! 9(1]1 x 10"'. < - 1~.I ~S 8 64~4.f- 0.000189264 11>< oom:lalion bctWOell1 from lorS<1 doh. >
),3.9 WorkInJuofDr i. rommon pno<.icc '0 provide. oorui.tent feed '0 • pn>
",,-era]
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" 'I>«ific conSlanIS and Eo i, the op«ifio commi"",ioo """"¥Y. '!be parame1 .. A "'1"'I'",n" t .... lhooMkal limi1i~ "a1"" ofT,. (see fig. 1.11), fot hard OTt< the ".1.. of A "l'P"'xim. "" SO ...... ,.1"" ~f A.IJ (tl>o im""" ,,"",mel •.,.) i. t1>; .k>!>< of tho T ,,,.. E c"".., .. zero input <"""iY. 'Jbe T, .... tIIIt" diwibution ruT\'< i. t=ful .. it i. a description of the p«><\UC1 'it< di!i1ribntion and tht T" caJl be c"",ide"", ." i,..jex of the dove<' of breal; ~, tht low" the Too ,.,J... for • gi,.. n input """"il'. K",,"ing the T" ,1Il ...... ult inl! from a ~,= input tho compk'" prodUC1 size d i.uil;rnoo... can b: calculaI Nopi".Mnnn .. a11241:
"""g:.'.
T,. i. u>U&lly bctv.~cn !()'20% and T,. ranges bctv.een 20-5(l%.
For crushing For llri.oing -
·, - - - - - - - - - - - - , "
-------~----~----~---:-::----
, . "• O.! _/
•
" •
" "
-- -
.,
• -. • --, -, •
..
•
"
.
,
..
.,
, "
, ,
--
,
.-.-
-'
-
, -. , .··
--
;, .' "
..,
,. S pee ~ ic
.
, " " Comminu'ion E.... rl/Y
,.
FilI, l ,lI,
N'pi",.M onn '" 01 (24] indi""". p" ..ibi< oor,"'.1;o" .... t"~n tht imp,",' pan>rt><;1or (A.B) ODd the Kond ball mill work ind<. ~"" by tho equation: A.II _ _ l .SW,
~
117
The o.t
(l.47) US<
in
_age
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"
TIle averqe size anaIy .... of III iron on: If\cr poT'im;"", OJulIbini sbowro. Po. ..I"" of 1113 microns This wa rod to • _ rod min v.hlbIe ..... lB kWblt.
"0'
,-
"~-
.~
_.0.
~-rt
3.10 A ",.. : nw;"" WJ\{lk of on: (_H.hll.S IIIIII) wu tnlObod iD ... imJ*'l _ ... "' ...... The "" ..... onaIysi. i. iiVCl below:
and tho pn>
Cum ...... %
"""" ".•
....,
m
~,
17.6
55 . I
21,0
u
"
EstimaIc: l. '('be ".h... ofT,. TOJ. T.. Odd T,", 2.
Tbe IfJ>"<.'ific oommiout;OII aWOl"" for Ibo: on: if A "'IuW 35 ODd B is 2.
HI AD on: OIIIJIple ~ 1.2 q and particle IIiu - 35.S min ratory impo<:t orudx:r. Tho,.."..., """ ~ and i. F""" bolo",. Tbe ""'" i..:leJc of the
."., wu 1).2 kWblt and tho limiri"3 val"" of\h: imf*l ~ 50 lid B is 1.R5. Eotimate the Too , ,,,,," ond okt"",,; ... !be ~pt' •.
"
[Him: AmIn>e Nopicr·M....n'. Eq. Or%) is applicable.]
~
""'i1'
A "'.... "'IoallO requil<'i in \be
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Chapter 4. Jaw C rus he r ~.
INTRODUCTION
The fi"t SUi" of oi •• reducti"" ofhard an;IlOfIlC 1"",1'1 of ,.",..,f·m i". (ROM) ore i. to crush .00 red""" tbio«s (hat .... It><> big f'" re«ivilijl IIoppers of r¥It. The meor "illi. II>< othon ope ..... primarily by !he: """ticillion of impact ..
im.,..,
u . D.. i ~ D of Ja ... C " "b... Jaw crusl>ers are de
surf.,,.,
'''ft.
mo,.. hen .... by • pitman for larger c",ohm . M the "",iprocalinlt oction Tcmo,"d tho movina jaw away from the f",ed jaw the broken rook panioles dip down, "'" ore again oauant . , tbr: ,",xl "",,·emtnt of tbo owinain&jaw and OTIISbed. 111;' jlp<::ni"1[ is rcy .... oompouoti,·. ly Io>o~r in c""""ity than the Bloke CN""" • .oo arc more: commooly Wl< ton of importance in dtoigniT\i the oi"" of primary crusl>ers, like • jaw cnuht.., ~,
(4.1)
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10.1
* 1,~ 10 1:7 * 1-7= Speed * 10010)59'1"" Frequen<)'of01roke,. * lOO - lOO
Ikductioo ratio, R Throw,Lr
or
10 praoctiot. tbt <>]lttttOr hu 10 okcid< OIl tbt ~!Ig of tbt tel 01 tbt dj ... N'1I" ODd. Thi.
oeuiIIa hoo 10 jnclo
the o",illation of !he _ cod of !he ja... , The ..... uf""'''''"" of jaw cnut...n pnwidet aU !be control. 10 adjU:k the ~e of IImalIer than tho opening <>flht .... Sui atl pOttibcr ODd \btrtfon: "ill al_)"I be <=1becI. lbt probobility P of • paltic\e heina orust.c.l or oot may be wrilkD ..: duri~
"') "') "OJ
- 0 • I
d < K,
f.,.. rOT
d> K,
- '-[ "-'j' K, _ K,
The val .... of K, IIld K" .... primarily fiu>criono of !he crusbet oct 1M at"" dq>t, fot
K, ·
levi"""
"""r.....,.-.,Q ..., F.. ""lur<.a
K" • tr.± b, L_ " b,Q "b,F,, - bo tu.n .. It, Lt wberc
tao. i. tho . ' of tho liner in boon ond t.-. i. tbt I...... length.
• K L & O.67L_
K, · l.tll
~
1.9X>nun
~+SI.67q"2H T(t)
±1.Imm
- the fno> > 25.4 """ in Il>e foed ond • on in\etpOlaliD,/l spline: 1'unctio!l ofIoMO/!"
( 4.1}
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'"' F.q. (4.12) ;r>di<~. tJ>.I the ca!»clty, Q,. iJ dirt>cdy proportiooaI '" frequency. AI ruter m,,,'efJlrIl! oflho jo..... ",,= .... ponicle WU»I foil the oompiele di!llanCe, ... during the IIaIf "",Ie. Q, was f.,..,..j Ie be inv.... ly pmpoJtional !O freq""""Y on;! coold be ..... " d by the relation:
Q, _13H3S W (2L_ + ,..""",,
Q,.
Lt)( ~)
- C"l*"il)' (fut &oquency) in tducI p
be,,,,,,,,,
The rtlatin and ~ty of tho jaw f op
Yc-
47
, (' -'J"
(L,r ~
• ,• "
.-, • > <
•••" "
-
""x 0/
" ", •
(4.14)
,, ,, ,, ,
•
./ a,
"
I
••
' 00 Freq uency (eyel..""ln)
fit- 4.'. Chanp of upocily ,,11Il 1I't.1""""y "'''''' J.... pIaIo _ i l l l to Eqo. (4. 12l ond (4. IJ~ 4 - 0.221..., W _ ).2 ... t.- - 0.1 0m. R - 10,G - lm.
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'" ., id inK ~f fine 'U< "" (he "fICMinK fao:;es of ,he j.",~ i. P'<'"",ted and will ted""" lhe l'I""luction raI<. The Off"'1 is II>Of'< matl
""">lw,,
'$IIH)'"
• •
For cootin""", manual fcodin;.. l, - I For """,im'::'''' IIl«hani<:a1 (=li"I!. k, - O.1S - 0.85
T oggart used
,II< wmpara';'"
red"".;"" 10n (tonne) to <>lim>\< the nu of the B I.... I)l><
cru.ocr T«juircd for a Bi,-rn duly aDd its prod,",'i"ity_ Tho ~= is Sc «Xl"",;"" flu;O of !he opcnIlion i. estimated from 5btained if "'" re\a'ion betw""n the <,."ul",h.. m... perc,,,' """ing (or rct.>iocd) for difTe","' .iu f~io"" i....umo:d (0 he liDhcr prod..:t indicott. II>< fair . ..umption of a I""ar In th< n~ a ,I>< cumulati,,, oj", diotribution of ,he onscalped feed 0« (u "'C an: ""'Iuim! 10 <'Iimale 80% lIlal i. PA";m: Ih""'~) il can t.. ......... I»" , implt &tII"ing ,V.c: of .... -,: W% .,.",;nw ,in: of lh< """"'lpcd f«
"""st,""ion.
(d ,- d, ) _ 0 2,<
'00
••
00
•-• ,. 0
,•
•,• ,• ,
0
00
00 00 00 00
,.
.•
• •
-- -- -- -- -- -~• -
•
.
,
,
•
•
00 SI... (mm)
Fit · O. L;""... '0/" ....... "'" <>f"" 1f>«l (b)ond """,alp«! (0)
i,
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'" (431)
E.:nc:r. Bn>maII o.:du«>d (~.
•
""pac; 'l <>f (lit .",sIt«. Q,
(432)
--
,,;c!th Qfth< crushing cavity. m Speed, rpm cOOSlA/lL d
Oft
the prop
In Eq. (4.]1), v ohould ht Ie" !han the critical ,-oIuo abo,.. "hieh the critical >peed as • Iimi:tiOfl of crushor throw and nip angle u,
(4.33)
-, .............................
,
• •• •
:
. ..1--
.....• , ..,. • •• :• •
•
h
"
......... .:....L__J
I.----i .1
c,
Fi&. 4.9. Step bynep iII"""ward 00 ... of """eriol thro~ .jaw crum.r [10].
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I 1 IJ'..
I•• ,J.. ••
,
! •
... '."'.,... . ••
••
~
I
I
i.
••
Pi .. ~.l I _ R.... "" b«,,~ l h""" ...t
oritOi:aJ
".
(R - III
••
• •
'-
'-
,
,
•
• •
b.'....."
f'il- 4 .12. Rei .. "", ,"",""ion rotio...:l ,,~IC . I speed (l, - ~ .OSm)
(4.46)
4.5. r~ ..·" Con ... mpliofl A numb« or "<)<~.,,.. 13 j, l~ I. 19]. ,,"W ,ri«! ~,S! case. u...c deri,'td ,'aloes .... .. t>ost.
"""",,,im"ion •. The mcthudslMSl comrnooIy us«Il
((l
)'ieklsat;,f""lOfY ... ",1.. _
de>Cribed.
4.5.1. Rouaruif.ng/i>h 'Ill< <, ,,,es,ion for computin~ ,he P'"'"£I COIUU1I1l"ion (PI derivc:d thromic.1l1 1»- Rose and Engli.h [9] im;olve0 "'" maximum ,;,-" of panicl., in Ill< disrgost of partjck. Taking the large51 si", of the panid< that should be <""'sed to aj.", crush
.i""
r .. -
0.9 x G, 0.7,10" -
6.3,10' G microns
(4.47)
wher<: u.. PP<. G i, in mctm.
At..,. to ..",bl i,h Ih< Poo ftQm tho l>r~"" prod"" ,i ... fl..,... and tngJ i,~ o.,...,i
L~ ",
and L, are in
7.0 . lo'{L_ m.
+ I.; )m,o"'rIJI
(4.48)
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113
,, , •, ,
Inl
P
•.•
~
•
St
"".• '" S, 01
2 ,~5
50.0 38.0 32.0 25.4
3,18
Si ~. 3 ~ .0
S. + SCI
~ , S, °l
279,0 88,0 70,0
0 ,248 0,028 0,045
•. "" , . • • ,. • ,.• •" , "
0 ,)3
32.0 25.4
S7.4
31. 8
0.32
C-2S.4 . 0.32 - 1.21
H...." by suMtirutinll in Eq. (4.54) th< CWT<1It, I. "ill be:
1- 14.2 • 0,0822 X 8 21 " 0,00305 X (8.2!)' - 15.l z 1.8Amp Slep ),
AssUmina IlIt "olliS< - 41 5 V. 1'0",... """"""plion - I 5.1 X415 - 6.3
~W
4.5.1. ,/Mtr..n D",J .\'''P;'' MWlln Tho mo05Ily been den.'ed ""ni Bond' , work in.dox. Whil, thos< pvc: sati,f""",'Y atim.>tiom of PO"''' it m"" be rem i.. tho POWdont on th< panicl, si", distrihLltion of the foed, Th ... if j ... ~ted 1M number of inknlll, in the di,tributioo of panid .. ohitt i. th
lui.'.
p<"''''
Pc .
;.,t Ee." .., P, M,
in kW
Ee...
(4.5S)
(4.56)
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'" O.7S
"
~LO
o~
O.w
13.0
5.2 2.1
"
Th. 1"''''''' requir..:l to cru<.h II>< limest<>ll< was 8 kW. E$1;ma/e tl>e PO"~ rt
,ho...,..,
4. 11 11>< ck»hh
I. 2.
n.e maximwn !iJl'I"'d, vc. at "hich it con b< op
v.la: S.G, of''''' Of<
• 2,~
RHERE:"o'C[S
I II
E,G. Kelly ..-.d D,). Spo1t;'"ood. J"trt>duc1;on '0 Minora] Proc ...inlj. Miner.tl
E"ii-n"i s...,.,.i=. 19S9.
(21 III (4]
WJ.Whj,rn, )",,","1 S. A. In>!.. M in. MeuU .. 12(1972)257. A.l . L)'IIC"- MillJ. [7 ] A.M . G.udin. f'riodple, ofMi ........ Dressinll, M<>M of Mineral !)re"im:. Jorn. W;I~y. I '!-IS. ]9 ] fU:. Rose and J.t:. t:m:li>lr. Tram, IMM .. 76 ( 19(7) C32. ]10] J. Broman. Engin=in¥ ond l>linin~ Joornal. JUDe (1m) w. 11 11 S. 10.10",,11. TJ , Napirn. in Communi,i"" Theory and Practi«. S, K, (od). AJ~1F" 1992.
Ka",,,,,
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1.11
MOIlIf rali!\j!. kW
16.8
".
83.9
,\cooroina lI:t ..-. btina ",pla=! by S"'" Sh"t\ model ,
',I. ), SeconJaryand r",;ary ""n< CT"'!>." Cone: c"",non .,ore ori2i.... lIy AAtrs, As \he mechoni"" of cntshirtl in lhest OfUsi>crs at< .imi l..- to ~ orn>h< .. thPOf1tor)' crust....... Fig_ S.l is • ",hematk di.gram of. 00fIe 01< muoI~ .. "","'~,-.,....., 1""'.Ild .... <,",n 0Il>..~. 1'1>< n"l"~ ""'" ..,gl .... 1'><1(» .... ",,,,in the j>IIl1kles Ioni<'''-< ,""'"ing....race. and thc",fon: pn>IIl1kl... To p,..".."t <1i of Ihe cruYltn an: I>
-~.
,,,,sho;rs "'"
Tho ~. ""'igrwl<.-d .. Sla"';"d 0_ n< OIIVOS of the tm-akiog bea,d, 11-.0 approximate distm«: of the annul .. Sf"U >1 tl>< diochari!< end desiifl"" lho , j-« of , ... «lics i. ~,-", in Tabl. S,4 for Ctu.t.er opera' ion in open cift.il and ck>std ci",.il ",,",1;"'<11
Fi"
~.J.
Sk..,h of.~' ""'" <,.
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erus.h.ion f(Jl" optimum u p.dty io: Q*
0.33 ~ 'in 9 (l""" + l_) II H ('in 9 - l' coo 9
-
-
-
r
(S,l)
MIlXimum dinance bel"-= I!}'raU1\II head and oooe.,,'< Minim ..! d i _ betwten 1I),.... i"1: bead and C<><>
O""ldio', o' pmsioo i, dimcul, to apply in I"*"i«: .. !be "",1< of ioclill41ion;' diJfu:ul' 10 me .."",. An easier method 10 o"imate oo.p.:ity ;. 10 apply the rnett.c.l ad_.ted by Rose and English f<>f jow erushen. j, 4.l.
Dr"""", Broman II 0] ~1oped an «pression f<>f the upadt)' of il-ntory cnuhers based 00 the some l"IIie usrd for jaw erushrn. r", dmvinlthe . """",ioo, Broman ronsi,,adl)' of . ijTOl
"""" "" "" < " -C_ C,
0
",lomc:trie """",ity of II>< 1!.'"'101)' c."II.n.-r. m' !It rrw\1l. head oot .. diomtter lithe di.eftal'llo point. m ok=dsn,m I prr minU1<, malerial con>W\t ho.,, ~. ,.O!U< _
...., 2 - J,
ongkofnip.
Broman JUSi<"" tho, ,I>< fre,qurnc)' mould DOt uk in a
5. 4. 1 Ron Qnd £"I{/i>h The theoretical worI< of Rose ond English (11] \0 determine tl>< copooil)' of jow eN>hm i, al.., applicablo to i)'raIor)' crusheB. A«Ob. Eed to dc:tcmti"" tho capacity, Q of iI)T1.'OI')' crushers:
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'" 1. Z. 3.
The "",imum Ihroughpu! oflhe crush
""",..,. ,,",i0.8 I. imc:.wnc:
...••• M
a
III
•••
42.0 18.0
partido sin: of SO mm jHru.!MXI in • oonc c""",", the product iii",
,...,
.~
••
~IOO.O
The po_ t<>nn ,,,.. 1.0 WItJ- Th. feed oj,., " ... then a llCrcd 10 on "v¢Ii", of 20 mm, ... product of O.S mm (m
con,,,,,,,,,",,, after tho chani< in feed size.
,..
A gyrlIIO<}' C""~ "'" itlStalied in • ifOloJ mi"" ",hc:re il "as <>
/U,d; us of the oonc.
2.
Change in throughput ... hen the
3.
"
A ""'" cruPCIlif'tll OCreet'l. Tho orosbc:r was expoclCd "' crush alllI< ral. or ]000 tIh. c.kullltc:
The 1<>'.1 at which lhe cOatge has 10 hc mainlained 2. Angleofthecrush
A "side:
~
crusher oj,.. 33-55 " ... dooillf\ ac«pI feed of ,j", 611 em • \ i8 om. The: <>pen oetting of Ihe diochargc oprninS "',.. lO.2 em. Tho rale of gyr.t1ion ,.,.. ns per minUIe_ C.ko1 ...: I. 2.
The oap<><:ily af crusher fur an occ
3.
.. the ........ ..u;~ If the open lide O
",'as
",,,red
tu
a ",'ling "f 12.1 em ""haI
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'"
-
6. /. I. RoJl O",iot, Sizes oJtd ()"II" 1be ... uaJ oru>her siza and pow'" rati"i' for ditTo",,, typc. "sri"". manufachlr~' lil
cr.
roll f..,.. .. dnchbed by
Toble6.1 Roll C .... her , i.." .
Sil
Crosbtr Surf"".
T~Roli.
Studded Rolls
'"
"'0 ,~
Roll OrU>ha-o an: arbitrarily divided int<> liib' and buvy duty beI"'ffil300 mm 10 610 mm. In 8...,..,..] I.hc sprin8 prOd \0 uperat< .t fo.k, .P=I< ~ to hero)' duty ron. lha! .... designed to <;>pont. at lower speed._
' 'm
-=
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'"
U. Opc .. 'ioo or Roll C ... ,h.n Th. (oed to ",II c"""",, is ",..II), dry. Moim.r. tond. to cI<>g the ON't..~ aD opor::di"". 1I0ne< dt). • ""hio, i, »'ef<=d. MIT-.:\i ....... wOter i; odckd b<.-\",«n
PfC'''"'
f,,.,.
Rock panicle> "'" ...... lIy fcd throu&h a eh ... Od to distrll>ule ,be charto .'-only .t"I'II! lilt "';J,h (!eng"') of the roD. Abou1 ,w(Hhird. of. roIl-",idth is acti," . ru in &Il)' cruw •. panide than the dislan« belween lhc roll. lend 10 p;o5S ~ unlippo!!" <\,,= 11'1< rollo. Due '" ,i"peralioo i l is .'-idel1\ lila, no middlings"" 0..,.._';'.0 is pr<> v,00>c opcmini ~ ore in ,he "'iion of 80-1 00 rpm. R~ulated . 'ow ral<: or f=ling ~ uV« ,<,'.,nly 11<,..,.. Iho: ", .. th of roll> i. prS
sil., ....
opera'i"" is odortcd ror fi .... prodOC1 .oz<.
.""fl
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'"
••
-........ I, orera
3. PII.
4. roll speoed and S. "'" .j,,,_ 6.6. I. e";"u;",, of~T", jng
fh;",",<
Tn operate ,ho II!'GI!. Polyoom grinding mil! the "...""re f«/\Iiml
j. oppiied
hyulicaJly
through four cylindcn to the roll thal i. d.$igned 10 me".., Imnlly, Tho ~ roll is ;lTIITIOVIIblc. The cru>hing I'f=I'l'" "!'JII;..! i, ~Iy of the order 0(200 MI'>. but for Iwf<:e required was in the rang< 0( 100 kN per linear meter of roH width. Sci,,,,,,,,, 121 hM ... i"""N """""",oily the sp«:ific comminution prenun: on mirJaal l"'Iicla lnipp .. ,
iii". , . . . ,. . .".
p · p(LOr'NIm'
(6.9)
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'" . ro
,f
! "
! •• fig. 6.1. P.... id. si.. of ~U<' from btll mi ll on
[I~l
"'I"'"'
rat._
A popular WIY '" des
(6.16)
Q · Q.DWVpp,
• specific ''''''''ghpulr1le. -
di>m
00. (1918) oxl=1"'d Ihe capacity of HPGR, in «rm, of the di,1MlC< the operation .. dtn";t)' of the IS :
=,
"'""'= ....
rol l. and
(6.17)
From labonolO
Ihe specifi, &rindinil f""",. F.. by. linear fun<1ion .f\be form; Q, -
",b=
l ( H CIojj F,l F. • C
- specifiqUindi"i force, - . foetor dtUI1
(6. 18)
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<_ '"
,.,
A ... of roli. """ "",wred to " .." ]nne.1Ont dolj,~ from • """'ndary Ct the ra .. of S2 u'h. 1bc product tbt con< crusher was 1= !hall 2 ~ mm. The prod ...1 ,ize from roll . " ... expt
,i,,, """"
1. 2.
the diarJl< - 1.6 tim '
0.. ..:
Speed of rotation - 7S rpm. Nip IIIgle - 2'1'
R£n:Ju:r;cr.. o; [11 PI (3)
[4J [5]
]61
[7J [81 191 [10) II 'I (12)
113 J 114J I IS]
11 6] 11 71 1 1 ~]
(19)
K. Scbol>1E1A1ME. Cb.ap! .. I. 19116. Pr. l"-J I. K. s.c"(If.:rt, 4'" T,wbb",)' S,.... Melt>ourn<, 1979, p. ) . l. 1'01),';"" Engineering Mad< by Pol)~ius. Report 2001 ),IL Friedrich and W. flaum. f'ro<< 19%. 1'1>. I H - 130. cm." Proceeding. of the Third Mill Opet>ton Coof.",ncc. A"'tr>I ..;m InrOncrt and 0 II.. " ""blod. 7A""",-KulHJ'PfM 11.193-1. P S61. K. Sd lllnerl, in Ad,'"""", in Mineral P"",e"ing. S~ I ElA I).1E. O\apI< ( I99S) S24. p. MO,.ky. ).1. lUe ... ui and T. Knuutinrn, P,,,, cedi"&, of the Intemalio",,1 Mil>Cfal 1·,....... Mi"¥ C~ CIoap1<1" K 19'J5. pp, 55 - 58, 1.11. Klyrool'w;y and J, Lill. in ComminLllion i'ncticc. S. K. K."at .... (ed). SMflAIME Lilli""",. Chapter H. 1991. pp, 9'f. IOS. KnJpp P,,')'>i .... E'ptl ito>« ..ith Hi;h p,.. ..1ft Griildi'3 RQII, in tli< I"", Oro lildU>11}'. pp,l -l . N. P.>Clky. Pr<.oc=J;"1I' of .... s.e.-rnth Mill Conf~. Au" ralMian l""ilUt< of Mining and ~1"'o1IU1'\iY. KJilgoorli<. 2001). pp, 4 7-55. J.e. Tn:mbky. Skill,,,,, Mining R"'iew. March (2001)) I, w. &um. N . PlIIZ
_,i""',
o.
Cipm>,.,....
19S3 .
,~
[20] M. Bonenby, II. IC.n........,...,1I an:l O. ~. In\<'ma:O>n&l ConE" .."" in E>
Oetobe<. 1m. PI> 159-165.
[211 R. Klyn>ov.>l
I'lom
N.
Pa/zcl~
J. KD
PI' 636-668. [22J S. MorreU, W. lim, F. Shi ond L TODIh.
~ or Mineral SME CmICn::oc., V"""""""" I, 2002.
and E. Burcbanlt,
n...ian I'lw:ticc lind Comol
i nComminuti",,~ ..
SlC Ko.waua. (ed).
SME/AIME, L.inlttoll, 1997. pp. 117_120. [23) D. M' ''Dft , Mina:all'ro 113-117. (24) M. Scd *:h and O.R. Knobloch, SME Annual MoetinJ, Den_. FeI>. 1987.
[2'J U. l,utjuhn and
1(. Scllonert,
1'1«' ,lings or xvm lrUmaIiooaI MInertI PI"'" " ;nll
ec..g:ra;o, Sydnor. 1993. PII. 161 1611.
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'"
-
-
-
Fia. 7.2. l obo l.. mi ll ')'1'<0. A
''''''OJ'' ~f 40 induotrial mill> in A••n];' found lhal ll>< """,;mum ball mill diom
.... ,"" S S.H m......nd 100000'h &,84 melers [I]. AIIIO!;O'I\O\I' mill. range up
«I
12 _ ... in
Jiamet.,.. 1hc knith to diomctor ratio indicated in Table 7.1 fOf ball mill. arc for oormaI use. Iu for primary ifiDding the: 1111", oould "ilrJ" bc\w= LI ..-.d 1. 8: I. For fmc: "'lI'iodi.~ Wldc:r opcn Oi"'.;l «Indilion, ,he lenath 10 ICS thai permit part;'l", hoxinll I"". ,han , .... size of !he V<" . to p"" throuv. but hold bock lorg« sized particln from ... torin, , .... ... , do"'II.uoam oompartmenl >0 tho, r""lIer ,j.. reduct;"" could tale rkac<. In oome in,Wli:c,,- thc: J ilT,,,,mt compartm<"" Jiff.",,,, ;ize. of ¥,iooi"ll boll", rOO" ""''' ~mcicnt griDdini\.
ha",
,;'.c,
ha,',
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,., How,,>-.., M"""n (1) 'm by: (7.1)
and W . lR .in9
(1 .9)
'" i, ii difficult to ~ the OlIil< 8 in perl be "-';1= io «mo. "(.adi,,, R and wiClh.
W, oft .... cha.lI< in tI>e mill ..,
•
I.....
u"'"
"I Mm
• • •
.......... .,. .... _•
•
w
I
.
,
R - O.SH. + O.!2SW'IH.
p .IO)
Tho;: r"""iQrl ofmill mlume <>«"';od by tbe'~ can olIO be ,al,.loted from Ihc: ....,.... IIC< mill cIIar¥<. tX. (~, of. circl
"f'''''
(7.11) Si""" Ih< om .. """tional""", of!he mill i• • R'. tbe "01""", Ih><\"", filled by the char¥< ww.ld be:
(7.12)
(1.1l)
and from the .implc rclatiooship< r""" Fig._ P_l) and (7.4):
H - R _ H. and (7.14)
Tbt ball mill filliOi ,on be estimated from \he i/WmOlI}' of the ball """ge at ..", Ho.,-",..", in teml, of Ihc: ong!o a, ball !lIJin~ (Jal ""'Y .]'" be oomputed .. i••Healed by Au";." aJ lS I. Tho.., .. I.'ions/'lil" art illo...' ''''''''' in Fia. ?S. The: chari" c.,,"re of va"ily may also be 100.led in •• ;milor waphical w' }' .. $hown in R a- 1.6. II.., is Ole from
dj,,,,,,,,,,
"'" om"" ofthe mill to Ih< charge C<111re of II"""!}'.
711. &111 size "11~iIi'" &11 Clrar~ Ball ""mm,,,,i"'), "".,lo1:>le [0< clwiina in i'inoJi,,>: mil" rona' from 10 _ 150 rom. 1"'" "umb<.~ •• il<: and rna .. of . ach bal l .j", oucd dc!>I.oC>' ''"lI. for
.j""
".-om out bzll • . In d<1.rm i nin~ the .iLo of bo ~ ls to he c tlarge< foed. Empiric.ally they ", 1>1ed tl>< ball size ... ith f=l .i •• by tho "Goati",, :
,. ."
Hall anllle , 9 50
,
" ,"
.-
""
""
""
--b
.
,L
o
V
0 "
m
•0 0
10
~ 0 .'
0.2
0 .3
'~ -
-
wm
J th 0.'
0.5
0.&
o.e
07
1"-
0.9
10
Ratio WIO, HJO fi l . 1,S. RoUt ...
be,,,,,,. boll fil l"'a (%) aIIo:I .,ill r&< di..... jo,1!
(~ l .
•
,
~
~
,
,ro
$
e.
,•
;; 25 0
" ", ••.,
-"+
'"'"
I
, ,
-1<
••
••• HelD, Hcog/tJ
•••
,
", (7.15) wt.
,j". em,
f
-
d.
- the ball dill'h
K
- . p"'pon;ooalil)" corul2nl do""ribod ...... grindability (""tor.
!he feed
f ... hard 0"'" lr.. ,'al ... <>f K " ... 37.4 and 29.8 for 001\ "'... Lowri"", [11111"''' • value of
;""""'"""'os im]lOlW1' opefllil\il
55 ror ,brn and lS for dolmlitc. 11>:: j!riOOabiI;,y ,""tot. K. ,'.nabl ... n.... op<"rating ,'''';..,1....~re iok."if, N [Of !he f...J as: l.
Wor k ind<:x
2. 1,
~
particle.
and fa< .... mill:
I. 2.
Mill di"",."" Speed of rotation (tT8
Rowland and KjQs [2 ) ""'si~ ...... ,-.,iabl.. fOf determining the IMgw ball ,;", that st.>uld be used LO conDIlCIIC< griodi"&, Thill i f do ;, (he ball diomelCf (mm). W, ..... work index of ,he maIcriaJ (~~'M). F.. the (oed ,i", (80'% """;"11 .ize in micron') and ,Ile ("",ion of Ihe critial [ 121:
d , _ 25 .4 [ whero
.!'<'<-'l of
I"" mill. th
(f-)" (loo,,(;_~1
Dr'
+<
lar~,..,
f']in mOl
[)
- thc;osi .... di.""''''r oflh
k
_ . """"'l/lt de,igna1
,,,,,,,tan.
oj>c of tile ball ma)' be
(7.16)
cO>! iron 00l 1. \be ,-.1"" of \be k i. dependant on the m ill type and the grinding eire"' I. The ,-.1 .., of k OS de\"",ir>ed by Rowland< ar.l Ki<>s 121 for Alli. CJuolmcn mill . arc lIi,'r o in ToOk 7.2. For "0<1
Of
Tabtr7.! IJalI Mill k factor 121
"_ Diaphragm
rn.,_
Diaphmrn
'" For calcuLtli"" of the dWnelt. of oylpebs, dc. to u..... replacement for boll., D<>erina lntemaLiooal [[31 pro_ide • • modifla! Bood fmmula:
(7.j?)
Tl>e .... ofF.d (7.17) i. illu'lntW in hom"l. 7.1, If the modia Ii.. form.l.. estimau a ball Ii.. I... ,han 25 mm or • <)1peb si .. \ns than 22 x 22 mm lhnI ;. i, teCOIlUlIa'Ided that lilt .i.. be j!'lCJ'l:a.I«l by 20-30% [I J ).
&""'1* 7.1 The ti .. analy.;. of . gold bearil\i 0fC crusb~ . Fwd"" size
Stol'l In this
c&><.., 1h< ..un. ind.<. and ball mill conditions...., \IIlJmo>,' n"~ mer lO ....
Appendi~
and find Ilia! the "m tnd.imun> ball size lO be chaJvd to ~nd L'" 0 .. Eq. (7.16) may be oppliod. as all til< ",1",-1IlIt ~ten .... 'lOW lno"n. The .. r"", ""bsliluting in Eq. (7.16) \he 1000t!l diOJl'lcl
is:
d
1- .4()sO)"[ 2S
2000 '
386,IU
78.(3.281 x 1.0)"
lW
• 25.4 x 2.39 x 0.739
- 45mm The . - oommercial b&ll size .,-allahl. i. 51.8 rnm (Ot 2.0") and woold bt """"IfCoghiIi ond de van
d . .. O.4K.JF - 0.4.31 . (0.2)"' - 63mm
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'" SlOp) AccmJing to A7zNOni'. Eq. (7.20). tt.. NflI""""""" di .......", of ball ,.",..Id be:
• U mm
The cl~ oi,-"" of oommerci.1 ball. mo.dt "'" 90 mm and 16 mm . The probably chooo< tho
Iarvr .lao tun.
opel'' ' ' ' will
715. Ball Wear Dwina a mill <>pCflIIion. Iov.mng of tho pow... =JWr=>dicatioo that ball we", ;, .ffCebout 2 %. Durini IOC ljriOOinllC ",0<<>, . . . (II< particle si= d imini$h ..... spo< if>e surfac. arto Qf the p;II'Iiclc. i""",o.ses and !he diamClcr of the ball dimini>hc:, " i th ball man The ball woar \aw. c.. th< ... r"", b<
.'.1)1
,,,,ted ..:
aon ,,-.'" '"
Boll ourfllC< orea [14 1. l!.all weor '" IlaII 1101""", [22).
A .... i" and Klimpnd [6.14 1 and Ro"'laTld j 2J] by ~j, i n~. theorrti,al buis to ,he bet,...,.,n ,.., c,"""I .. i,.. .....,. ["""ion, of b<.II. charged "'lh their "..at. To deri.~ ,1>0:
,eI.,,,"
I. 2. 3.
Boll w= "'" equal to ,he .,.. in boll maso. Boll "eaT ""a •• f_ .ion of ball siu. Frtsh ....11. >0: same chorac,erU,ics.
U'in~ ,hi. cooccpt !hey dc'mnincd the c~ in a &rindin& ')"(<111. Ae<:
'"""II" in !he en,i,. sin distri"'ion of 1>011,
"""in ""'" f"""ioo of boll. in the charge d.. to ,,'."" is:
01 [51. tho c"""g< in tho cumulat i, ..
dM, _
"
,,"'hm:
(7.21)
M.
- Cum"lati,.. rn... fract ion ofbalb of size r in ,be c!wll".
m,
- M... r.1< ofrq>1aceme", boll, per uni, mas. of ball ..
nlr) - Cum"lat;,,< num ber ,i", di,lrit>u,,,,,, of ball si"" roJi", r. fir) - ball"~"'(o .• fw>etiooofballr.>di ...
'" Po
, who",
2.
- S.G.oflhrball •.
1bc:tcnnK,,,•• ddincd,,,:
K _ J.!,dm(T) ~'
(7.22)
m(1) - 1h<
Tho n,ake up ... 11.
mal~
,j"" ""'" coo,iJ.:r,;-d . och (~, (he si ,.. ""AX - ,,> r, >
up f>. > ... >
' . ~ ,_. and (7.23)
j.
1'0< (he ",.1.. op t>oll "umben, " , ,.n,. , ..> .... .., \hOI til< "con..... di"";""Ii"" ~f "ll5 of . j", 1\
i1: (1.14)
(7.m whero ~ could ""I'e
per unit time. Eq,
"th.r. 01 ""'I,"i,'e ""] .... can be: ",·",-';n<1l os: pmi'i~
(7.2~)
and ~ WlIs equal to
u.. "=di"",,,. (7.26)
TIle "ear
""0 oould a1"" be "Tit«" ,,<:
(7,27)
(7 .28)
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Table 7.4
Com...-;on of flail SiH Ui..nbution (25).
n.,
~
,n
149.5"
00.'
3.57 4.61
'00 •••
,.~
14.0
'" w..••
2.1S
26.0
0.19 0.11
,,••..••
"•.""" '.000
,.•
, '"
•••., ,,
,~
9S.0 100.0
7.67
~
20.1 47.1
~.,
~.,
75.4 11.8 IS. 1
"' 17.0
n.4 4.42 10.0 12.2
13.0
M'
95.1 9S.7
'00'
'"
48.7
0.425
".•
20.1 47.1
S1.5 S3.7
12.76 16.46 21.24 27.39
~ .. w.,
Tbo. 81% will be 11 4 """ b.n.lIld!be n:n will mW: up LO 13%. N.... l muhiply 001""", (lJ. Tabl. 7.3. by 0.17 for edI LOp boll oj", lIld lIIlWIIlolali"ll !be feed ball oj"" distribution n:cordcd in <01""", S. Tbot io:
23.0.17
- 20.1
(31 x 0.17)+20.1 - 47.] (l ~x O. 87) + 47.l - 62.7
"".~ Srep 5 for
o:alo::ul&l
-
4.42 10.0
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'"
,
" •,
~
, S.II "111"\1. J.
7,1.9. Mill Co..Ji/l"", IimaIc: of ,undilions i",i
Table 7.5 Erred of mill spcn grinding action (27)
% Critiool Sro i
"
W
m ~
m 00
m
W ~
Sliding
,, ,,, ,, ,
ClO!<:ading C •• lrifuging
,, ,,, ,
,, ,, ,
Tobie, 7,S ond 7.6 indicate thai I"" opIimum wr.Jiti ..... "r l!rioJi"ll
WQU]d
be bel-.=. 7li-80
% of the critical ..-d ..."- • ball clI:ot~ vfl.l-4S% of tl., 'nill ",I.. ,,,,. It i. vt....wJ fAA" Ih
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," Stop 2
The critical 'pox
V, _
423 ~J ,O - \UOI
', . • •.
rpm
th
Mi ll capacity con row he C
Q _
,"""',!oIi"" dOlO in the: F.q. (7.46):
6.13 .<3.0'" ( " ) 7.9(0.35 - (0,937.0.35') '{ O.gS- O~~:~~,) 3.0 \ 2
I d17XlO(-~ ,,75
I ) .120000
- 21.ltih
Mill Capoocil}' for Dry griroJing 1'0 obdcx from W", GriOOinll bdex multiply Vi ....,. by 1.3
In
,.i, caoe ,hon:f(lft". ,00 ,,<><1< i.,... for dry grind;".;: - ilJ" I.J - 11.8
~ \I'M
Subs,j'"';ns thi, ,".h.. fOf W" in Eq. (7.46): Q
(drygrindin~) - 2L1t1h_
Eq .. (7.46) and (7.47) ,an help an <>(>Cf'Uor to control mill prod"",j,-ily. FOf .,ample, comidcr a mill of diomctP<"'atioo . M It.. feed particle o~ dut '" • ,banI!< in mine operatio .... Exami"" the dnng. in mill ~ity. oi l othcrs f"' tO<'! nomaini"ll u....,.... tI. !he mill .ito i. 1<1 . i ", oJe,:n:»ed to 250 mb",,,. lbon to 125 mia-om or..! funhe, to 65 micron •• then Fig. 7, 11 is drown us1"1! Eq. 0.46) to doet.""i". to< , hong< in m;ll """""ily "ith . 'hango in fom , izo. Fig. 7 , )2 simil.vly i, drown to ill"""",. the e""""It)· duo "' changing doe""",", ofprodu
.i,..
.ff"" ""
7.4. Mill Po.. u D"'..··.\I"'ba.i.. I .\I ....... "The n>OIot power ""Iuirtd to h"" • milt r""",.. .. '" the "I'<'"",in~ .P<¢d is «l '" include lIIo initial .tanin£ t"'G "" and rnechonical an ... g.~ts (0 rotate tile mill. Attempt' '"
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,., I. 2. ). 4.
S.
Mill do...,..,..., Mill length, % ollOl~orballloo.din3 .
Mill 'IIOC
p~ a 2.4.nA8CL
- mal -
-
(B4) PO"'~
;n k W.
• foetor of .... mill diameter. • flroclOt il'll:
• • r..,tor
- thc mill length.
Nunlbcr¥ take; thc mill di.vncter Lo be !he insid< Ii"", di""",,,,, ....,jell A. II ond C in tabul", fOrm but are ICI . .",,,tal graphically in Fiil'. 7. 14- 7. 1S.
=
-
7f+f
,oo
<
•
• ••"
;;If
~
,. 'oo
• •,
1 1
Fii- 7.14. NfH'd ..... rae"" A .. .
7 ,
IU
•
,
fvn\:,"" ofmill dw.-, [9J.
•
,
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," MilllD > 2400 nun.
2.
T<> '''''''''' fQf thi •. Il<>nd intn>dU<'Cd a foetor crib«! ...
,n. slurry '" .1""'1' foc'", and
ddined it n:
,. ", ( ~ s.n-d . . ,I 50 8
(7.61)
' • L1 _
"here tl><1W1IIi! mill. of
3.3 m. The modif!ed !J.ull ,;;0 foel(), i..dded to Iiq. (7.58) owl is ah... as:
r _ •
1.102(""'" -IBD) ,W'
(1.62)
50.8
where D i. in mctcrs ond ...."" in rrun.
l;q . (7.5 8) oppropriot.ly modir,od by l;q. {7 .61).md (7.62) l"""ide • "",""",,",Iy go«I
indication of mHlI'O"~r ot.>:,,"'cd in practkc_ In order 10 determine the 1'<'''''' requirtd by dry gnu. "i",'=lIe mill. E'I _(7.SS) lhookl be multipliod by !he fa<."lor 1.011 and for ,,<"t. low lewl vale dil oompa=! "ith thaI fl'OOl Boo.h cT',od!hat the f,ac,iooal fillin¥ at ",hich a ball mill " no,... !be ntalCi"M" PO"" could dilfer. Ru"lond.md Kjos 12.21U2J ha,... pplied Bond", F.q . (7.SII) and ,""<$led a ,lightly modif>< I"'WCf ~ui.....J fOO' ",'"
.
,,<(1- - 0.1 )_ .•
!.L . 4.879D" (J.2-1J" M
>~-I" d
kWIt·bo.ll.
(7.63)
Eq. (7.63) i. opphc.bl< for mill 1"''''''' ... imotion. of "'''' grindin~ mill. hasi"i diometcn gr.:al
cor=tions ore nt'm:tioru OWl)' bo!Il f", boll mill and rod mill grindin~. COI'1'eC1ion fOClOrS ,uggesled by Ro",'lond and KjM [28J Ihal apply for bo.ll mill. "'" Ji,-en below. Com:ctions for rod mill. &1'< ,i"," in Chapter 8, I, 2.
Correction for d!y grindi"i" Bond', work iodex i. cortiod oUl under Wet cO<\dilion<. C"""",ion fOf "et op
),
o'.... i"" corrt<:\ion
r"""" is defined a,,,
.i« gr.:.tc, Ill'"
the opllmum ,jzc, 1lte fee
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,. Then from Eq. (7.~S):
f::rIrmplperaIed II 70% of ilS critical speed and tequirc.J lO' The ....... oftl>< l!1indh'lI media The .... mill PO"'" roquinxl to oper"~ the mill PO"'" n:quinxl to ~rinl in
1. 2.
'n,.
J.
a""",,·er1low mill
S
St
SuMiluti"i do .. ¥i'''S: - (3,1 4 159x2. 1'/4) xO.4h2. 1 x 7.S . (1-0.15) - 1M !
M. SICp 2
1\, the mill d""""ler is k:s. lhan 2.4 m, Sub"i'uting do .. ,-. Ioc, II;''''''
P
•
w
~lep
US<
Au"in', Eq. (7 .6'1) 10 calculate tile .... mill p"wcr.
110 x 2J" (0.70- 0.1) (l-({).9J7 x 0.4$») x 16.6 (1 +/5.95 (0 AS' ))) ( I + <>p (15,7 (0.70 - 0.94))1
• 95.6 kW
3
AIt
[or •
fO . ) . (),().IS. 0.45)+ (4.55 . 0.45' )-(20.4x 0.4S ' HI2 .9xO.4S' ) ~ 0.962
,111"" "fV -
'"' ,
I.
1"'''''''
To compute the f'eG"i~ foo- gtiOldit\i; in • ,,-'" o,-erf\ow mill, Au'tin' , oqua
9H. 1.07 - 102.3
~w
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10.1
'.
: 0----~. 0 ,, 0~---c-----~., O J. : l oo.. • • • • • • • • •
:•
l e».
•
,
,
~
,
.
u
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.-.- . . .-... . . ... -....... . ... ..- . ...-...
'-.
..-... ..... . . .
1" "
"
R
o•
wb=
.
"t
-
tar\jlenliaI .... locity of . partido I....
PC
-
in """ lind daWtycflbelQtlJ
.,ed II any diJlanot R from Ibe """In;
~
'"'" of puklltiol """'lIY (PE) IkYdup.d in Il>c: porticloo and boll> ,,",old &pcnd <>II tb< brigl>t \0 which !hoy .... raisod. [fthi. bright illl ilion !be -.cia1Cd pclenti&l """'iY -.ld ~.
(1.72)
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107
'. ~
2~ - a ,
+a,
". " .[ -( ,
_
=
(1.14)
onJ
2R,ina , - oin<. , )
j"
(185)
.."""' R i. 1h< "",on radi .. po,i'i"" of ,"" "" i,,, part of ,"" <~II" 000 f""" ion of 1h< mill volume oc
J,i,....,
i, ",b,ed ' 0 ,he
(7.86)
The fr.>:)w 1h< J'O'"<>":ty of the cn"'1tC. \be pulp <: "-"""'p<;om the: derWty .,fthe lOl.1l chari" i, by'
J,i'''''
(7.87)
t""
lhi, US"'" n:quired by \be <)'Iindric" and ''''''' portiOll is cak"I"""" The total 1'0"'" "'I"ired b)- th< mill i. (iI<-n:
,"3l""
I' -
[No load po ..·... 1 +Ipo"'",. d¢lennined 1»' Eq •. (7.80) • (1.8 1)]
,hi.
Mon- ""'""
«!au,'.
(1.88)
~
<001,,,,,,,,,,,
well "'ith ob.erved in1
7 4 0, EI""dc"} llriw 0/&11 .\fill. For driving a ball mill. Rowland and Kjoo l2J recommrnJ lbal the oonnc!>wId be
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(27) Aoon, Nordberj; Bulletin 315, Mmy MiU [)jv;,joo IIIkl Barber G=" T«h 1luI1. &2().. 91'1,1970, pp 1- 11. (2gl C."'. M"",lond ond n.M . Kjoo. in C"",minulOon 1'Tactices. R.K. ](a..."".. (cd). SMEIAI ME. 1997. pp. 319-)31 (29) H.E. Roo<. ODd ItM.E. Sullivoll. Ball. Tub< aOO Rod Mill .. ConwIbk. London. 1957. [301 Doerina in!ematib<.~ 10.2003, (rom htt~:II,,""W.c)'lpebs.oomImahlk<>
[31) C.A. kowlODd. I~"" ,ding> Tenth Int
Conw=,
1321 C.A. Rowkw>d ond [).M. Ki<>o. I'rincipi., of Minero! """","sing. P.
~
(ed). SME
IAlM~~
199'),
M.J.
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8.21, /I,>dMiliC/o(I'I;t Rod mill
usuaIl)" ocrupy about 45% ollbo intCIlI1ing bion of ,he rod.. The .... ij;h, (Of depth) of rn0t< parallel ""he <""lIal ."i, and th< body of th< mill . Thi. i. "'" always JIOMibi< .. in practice. p""'H.l ali&fil'\< lI'in.di n ~ <1''''/'&<. , .... grin.di"!! ehatot,";Slic. i. impaired. The bul~ density "f .. "",,,,' rod dor the am< oon.ditions o f op<,"'ion th< bulk den, ity "'<>1M he S.4 tim' fOf • 4,6 m di>or>elt! m ill. Duri,,¥ ..... grin.ding. Ibo pulp cl\aJ)led 10 II'c mi ll is ",'''''')' hdd be,,,'«" 60 - 75% ""lid. e~
10.""
1"""""" """"
,,,,,,!I.
~R HU~ gtlt
Rod 1mi'M
"".ter th,n 6 """t! "'" ""Idom trul)' , traij;h'. £len' rod>
promuI< !an~ling or.d
should be , "0>Jed, The rod dim< ",. ..,n fo< ,hi, i. at hi!J,hcT . p«ncr!han ,ho in.ido: "'<>rkini length of "'" milL Rod. have. rell 12 1 the m;ommtn.ded ""io of rod 1."lIth 10 mill "<>rki"l! d iamrt
,peed,
.""'1)'
Re,...n .......... loaM , .. len~th as a raull lhc rods in.., smaller ' < rk ir.de_, 0'" feed . ize W.. ) and II>< dco;i,y of"'" 0 ... R"",laod aod Kjos [2J co ... i
"'<"'"
""'ok' ha,'.
""e
"'"n
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~
=
•1
~
300
•
0
= ,00
•• Fi. 1.7. EfJoco ofJeClL><1i<>o. raIio
.u,
'. · .. · , , • ·· · · · ·. .. · · ··. · ·· ·. · ... ·· · · ·. I · · •.• • ·. .. .... · ·· · ·•· · ..· I I · · · ·. ··. ··· · ..· •• , .• • U ·. •· · .• · ·. · . · I ·. · , I."" • .. · ·. . · ·. ·. ,U, • · ·.. ·. · . · . ·.. ·. · ·• 1., , '.' u ,u
'j';: ~1
r
,
....
J
" _it)' of rod millo for d ilfcmlt .. ill dimen.m , (d'utwter
n.e ~ of lArger mill..... """" oenoiti.... to ..riool. fii-. 1.7 mow. \hat rod mill ca".cili .. varied with
in....... I~ .. 1he !<>duction rvio.
1. 2. 3. 4. 5.
UmiwionJ mouel milb 10 prod..,. porfecdy lnip. """,I J<>llo Swellin& oflbt ollarll¢. porIioularly ..... the feed end lJ>o<-. si'\il oluny density ..... '" 1000 o r _
Tugl~
Fonltyh","OJKI liftors
J.4. Rod MYI r-.r Dnlt Ju in t.ll min.. tbe p<>ww
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n.. optimwn fcal llin lUi", F -
,,,I by R<>wlmd and KjM [2] fun rod mill iI:
. 16000 [ 14.1 ] " W,
(1.12)
The val"" of W, iJ bnt tak"" from "" impo!l"l "'.. or a roc! mill ifindability tost. whiclI .>"tr ;. tho i""""'. FOJ' boil mill. II>!: vol .. oflht COMWU ill Eq. (8.12) oquol. 4000 ~il\I to
RowI&ad ond Kjos. [2]. Tho cotTCCtioo rae.". r, iI [liven in """'" o f _ iId
(1.13)
w'-"
R FOI'I -
11M: .... ""Iion nlio optimwn real llin
i. "'" ",,!.nmJ fOJ • t.ll miD fcd by • IUd mill or ifF, ;. ""'" u.... 1.0.
nu, _
S. Com>ctioo rm fin.cnou of (!riocl.
A eor=tj"" f""","" fm Ii........ of a:rind i, owlioable wIl
,
,
.
PO! • 1~.J lHS PO!
~ IIw>
10% of tho
II1fI'II'd
(1.14)
6. Cormo:Iion fur _iun ..00 (ltno. or loiglo). 1bi. corr«:Iion i. "";"ly for low .... octioo ruico. The ~ focta" F.. !ItCd "'" be opplied if;
-2 «R _ k ' )<+2
(I. IS)
R' a ll+ &
D
L.
- imp ofrodo, in ID
D
- irIsidc lintt diomet
Corr.ctio
F. i ...ti_Lcd uoin8 lIM: cquatioa:
F, . l + 0.0067 (R - RO)'
(8.l6)
Tho """",\ioo i. not ol"·OYO nee<\elj for hip .... 'IC'ioo ratios lou! b U>Od if Wi for II>!: rod mill and bo.ll mil! i. il......... thon 7.
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Grirdabili.y ,""", for.he ball ",ill ProdUCl sj"" from , .... ball mill
- 12,Ok\\'h/1 - 150 microns
Drtermi ... d>e size oflb< ball mill opcr.>.oo in dosed ,ircui.,
SoI~liml
S,'1' '
The diocharie from ,t.: rod ntill i. ,be feed to the ball mill. n..",r"", in this c... the: """"', W, .. illl>::
W _ 12 .0x
10 [~_ 1 1 "'" ,,150 JIOOO
- 6,0 kWh.'1 S,'1' 2 Condex \"Oh.. , Correction faJ F, do 1101 OWly C"""",ion factor F, "ill be ookuL>.1ec~ for [:
.ft"
""<""l< "'""lI
F""
~ 4000 (13' I'I )" l2.0
_ 4,.l67micron.
The f<"ed . ize (1000 mOerom);' k,,!han this optimum food oiu, thcJ<:1On: tho CO<'l'Ulion
does no' have to t>o """l iOO. CorTeC1ion f""OT C"""",ion rOC'Of C<>rm;,;oo rocto< C"""",ioo fac"'"
F, is not opphcahl< .s in thi, , _ p.. :> 7S micron .. F. is dOI awli«i as , .... =luclioo nolto i. ~""" llwt 6 ( IOOOII Xl - 6 ,7) h is "'" al'Plicobl<
Step 3
Mill Po..-er ""I"ired - 6.0. 200 - 1200 kW Sl
To e oornmerci.Uy .,'.ilab!. bal l mill tha, would sui, ,I>< cor>di'ion.. ,..fer <0 the monuf0<1Ilm" S litomun:, f"" example. Alii> Chalmhcd by Rowlat>J and Kjos {2{, From l" tabul. "" """" mill dWjl<' . tId ",hot ,h>tO
t'"
['oi l milll..,~th Boll mill di ....... ' or Ball mili lOlld
Ball c~arg. mas, BoI l .i",
--- '"
• .17 m 4,57 m (imide
-
III , Mmm
Ii"", di>m<1e, - 4.39 m)
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I. 2.
., 1.
The ca"ldl y of the: millllOlkJ city and .... jrindlna condition. 'lbe powa """"""pti"" .. !be pinion IhaIt . - dry IIIliI .... oor>:Iitiom The opec;fl< lIriOCinll ~ wukr dry mel W<\ CMditiooo of grindlna.
"Tho tefI......mr index of the feed to. rod mill .... 10.1 k Wh!\. !IO% of the: fotd 1'"' .... 2 mm and ' 0% of tbc: produn trom tho min 1'""..... oW microm. The .,ill dilll'O
••
Gold ore """ cruahod IIIOCCSSivdy in • primary mel thai ill • oo=odary CNSber. I'rndIlOl trom !be I«XlDIIaty Cr'lWlcr OI _ ind
I. 2. 3.
The I'
Millcopoo:ity ( til)
Data: (lulk dtnaity of""" - S.611m' I.D, of!bemiU
- 2.'Sm .
••• CruoholviJtQ; • maximum diomeler of 70 mm and "",,I}: 6c:w.ity $,6 11m'. The mill ..... openUcd .. 1$% of tho aitital speed to JllQloo;:e . tlcady prodOCl oize of lI1icroru from I feed si:or of 1200 micn>ns. !'owor OOIlSUIIlptiOll <>f !be mill ..... 1.7lS kW.
r.oo
&I",,,,,,,
I.
2.
The rod dialncltf III o:rmmtfIClO of crushina The rod length
0..10: '" - 4, S 11m'
B, 1O A wei oV<'rll<>w rod mill WIU """ ed '" 75% of tho orilical .p«>d and found to draw '.S kWIt of rod • ......., tbc: mill w.u k...scd 10 JS% of il' ",Iume. A certain nllTlber of rods were then ~ 1IId!be mill power increaoed to 8.9S kWIt <>f rods.
L
VolUJD< of mill <><><:Upicd by the new char¥"
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Mill, ho>lng equal D and L (~mil!!) Mill, ..;th small DfL ratio or hill,h UV ratio (Low .. pect mill.)
Mill. _
=-,
llIL - O.l) • 0.66 (UD • I,S • 3_0)
p
.. pect mill. ",jth oonk. 1 end, Of< ..,.,..ime .. f~ to .. paltCG" mill, while ",;n, v.ith "'I""'"
Some dry 'U\O~oWIl as AaofaIJ milb, Tht Cad;" Hill (Aostralia),,~ SAO mill i. 12.2 m in
with I 20 MW motor and in 2004 was the larae!l diameter mill in operalioo in the ""rid. Mill sizes up to 13.4 m diamtructr inside liner I'""th. 1lw: mill i. op \IS< ",mpo"''' linen with lii'lcn at thr foed mote """""in .. ion by impa:< and attrition inst
..,,,,,,,,hat
The dischari< ends ore fittelonina OUt of hiah·sp«:d mill rowion in the .. ~ion ........ the -'JlO
prod"", ...""
.p«
F i ~,
.x....
9. ' . IIi", a_ t .. tOo A{1SAG milt
v.-iIh pot,"".>oJ """"",I 0nd,.
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u.", aspea mills lilt besI",il
mill • .... """" commonl y ' - for compe\< ''''i''" diam
9.2. Op<"'"'"
of A(",JSAG Mi ...
9,1 1 F..dSiu 11>< f~ to high osp«1 AGISAG mill ........ ually p",f....-.d from lI)TI>tory crust-..B. "flile .... feed 10 low aspeC' mill' .r<: po-dc~ rfOlll gy"""'Y ""...... i. """'" 300 mm oM fr<:>m j. w cru,he" i. abou, lllO- loo mrn. thu. the .",umum 10ed "'" may be ulon '0 '>II¥" b
mm.
"'ceordin~ to
MacPht""" and To""" po ...e, d...,,· i. IlivCfl by tho K lation:
171 the op(imllm r""" 0;"" con,;"'"' "jth m"" imum (9.1)
- f~ 80% l"""i,1I. .izr in mm. - in,iclioru bre .. tho """,ncr panicle. but ..", breakdown ,hom",I"", and , . i, ,be mill as ,xodutl . In due Ce. , be on: ked ed at deept, 10".1 . , Thi, " 'ill a lto, ,he bal."". be.wee" th< lump wiooing media and the solter com"""""" of the ore a. ,00 Jt.nkor l\lntflS "ill breakdo"l1 """" . Ioy.-Iy. CoTaduall )' I...... fore. steel ball. " 'ill ha,. 10 be ch"'¥<'i 10 help breal,be _ com ..... lumps 10 ...,.i" , ... balaoco .... ,n,"nwn thru"jIl'PI'I. ,,, II,,",' oo",,,,in"ioo proc<'" i. gtad ..... ,y by the ,~I ball .. 11>< nurnbcr of,,,,,,. ball. and .... i, . i", depend on 1hc hatdnc.. of 'ht ore . .... original Ort Sil.<: ond II>< si,o di>1ribo,ioo., IftC ..... in>; tht ball ,i« and d< oll-.er hand iftC"""I"" ball numbers iTl<"""" the I=alC,use. II>< thn::lUPPI'I Ilonce a balor.ce be',..ee" II>< nwnbe, ..... sl"" of balt. is "'Iuirod, Ball size. used ....... A""",lilUl ooOOilioR> rronnally ""'ge bo«>",n 100 mm 000 12~ mm "'I,h • m.... imum of 17~ rnrn. For ore, lilal <..II}' clisintei'8'" (< '"'Iuirod tonr\Og<, 'Iho ..Ie of brr:ok.~< of panicftCC brtak.oJe , ..'" A, ,hi. point ~e .""""'iaJly &om .bra the modi. siLeo b",aug' flI',," i""",.", agoin .. impoet
"'on!., ....
I.... 0''''
n,
....
""",tl
"'0,
d.
"""'ts
hlIlY 10 n t; n"'" ' ho II,i n ,vl"me 10 calc"'. " the char&~. E" imarion of c),lioori<;.1 mill .-01"""" i, "" probl
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-
~- 2.JtS::"~:::1 f"~_;"'83
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2.
J, •
],
~t. .
0,8.
Au.tin ",sse", th;,t the mill po"e, '" obI2in (11) hu ud Ed",3fd,' 1<>. work """ limited 1<> a f,ow O....T ....tioon< only_ '" ob'
, -['-''''' ("'" -'ll(-'1 """
(I ..)
P.
(9,18)
1A
ToXing 111< ,"""",,,,,,Mod ,-. IL1< of A .. 1_OJ . Eq . (9. 1I) mtnsfomu to:
(9.(9)
The follQwing gc,..,raI ,*"",,111;"",
C2l>
be ">ad< on mill power coruumplion (3):
I.
Sintc mill p<>v.tf is propo~iooal to 0"'. ~ diamtl., mill' "ill draw"""" POW"," ,,",' mi ll volume ,han >mall d iame .. , mill. . How",'.,. long m ill. (low .. ~) may''''''''''''' more po",e, than hip:osp,
2_
Diaphngm m ill. d,aw 16% mol'< POWC1lltio .. it is ......110 i...... l1 lO--21W. ""',,, power", meet ,"";at;O'" in load primarily doc '" clwtgc in ore ,hal'OOTeri"ics, dargi"ll rat< <1,_
1. 4.
11"'"''''
9,J. /, /'I,,,,,,,,l&;N (Rtf",;.".) Mill P".,., For de,ign and .,.,...-.tins P"'1""'" il i. otl... n«<'5a!)' '" <0Tll~ ~ bct"U'II mil];, A < COO«1't of """"'li>eJ mill po"".'. Au"in dcri.'ed tho exll'<"'sion for normolisO
