Ch 12 Rod & Ball Mills

Chapter

ROD AND BALL MILLS

By: Chester A. Rowland, J r . and David M. ~ j o s , Mgr. Sr. Process - P r o j e c t Engineer Gr inding N i l 1 Process Development Engineering & Special Eqpt. Appl i c a t i o n Mining Systems D i v i s i o n Mining Systems D i v i s i o n A1 1 is-Chalmers Corporat ion A1 1 i s-Chalmers Corporat ion

INTRODUCTION

Minera l o re comninution i s gene ra l l y a feed prepara t ion s tep f o r subsequent processing stages. Gr inding, the f i n e product phase o f com- minut ion, requ i res a l a r g e c a p i t a l investment and f requent ly i s the area o f maximum usage of power and wear . res is , tan t mater ia ls .

Gr ind ing i s most f r equen t l y done i n r o t a t i n g drums u t i l i z i n g loose g r i n d i n g media, 1 i f t e d by t h e r o t a t i o n o f t h e drum, t o break t h e ores . i n var ious combinations o f impact, a t t r i t i o n and abrasion t o produce the spec i f i ed product. Gr ind ing media can be the ore i t s e l f (autogenous g r i nd ing - pr imary and secondary), na tu ra l o r manufactured non- metal 1 i c media (pebble m i l 1 i ng ) o r manufactured metal 1 i c media - s tee l rods, s tee l o r i r o n b a l l s . Th is chapter covers rod and b a l l m i l l s which u t i l i z e manufactured m e t a l l i c g r i nd ing media. Fig. 1 shows the cross sec t i on o f an over f low r o d m i l l , F i g . 2 an over f low b a l l m i l l , and F ig . 3 a diaphragm (g ra te ) d ischarge b a l l m i l l .

MILL DESIGN . , .

The i n t e r i o r ' su r face o f rod and b a l l m i l l s exposed t o pu lp and/or g r i nd ing media a r e pro tec ted f rom wear and cor ros ion by rubber, metal- l i c o r a combination o f rubber and m e t a l l i c wear r e s i s t a n t ma'terials.

Rod and b a l l m i l l s e s s e n t i a l l y draw constant power, thus a re w e l l s u i t e d f o r use o f synchronous motors w i t h power f a c t o r c o r r e c t i o n c a p a b i l i t i e s 'as d r i v e motors. A n e t o f approximately 120 t o 130 percent o f running torque i s requ i red t o cascade the charge i n these m i l l s . The p u l l - i n torque i s about 130 t o 140 percent w i t h t he p u l l - o u t torque t o keep the motor i n - s tep ( in-phase) gene ra l l y i n excess o f 150 percent. When rod and b a l l m i l l a r e s ta r ted across-the- l ine the s t a r t i n g and p u l l - i n torques r e s u l t i n in rush cur rents exceeding 600

240 MINERAL PROCESSING PLANT DESIGN

. . F i g . 2 - Over f low B a l l M i l l

F ig . 3 - Diaphragm B a l l M i l l

MINERAL PROCESSING PLANT DESIGN

percent which r e s u l t i n poss ib l y h igh vo l tage drops. To d e l i v e r 130 percent s t a r t i n g torque t o the m i l l t he motor design must take i n t o account t he maximum a n t i c i p a t e d vo l tage drop. Motor torque decreases as the decimal f r a c t i o n o f t he vo l tage a v a i l a b l e squared. E.g., a motor r a t e d 160% ~ t a r t i n g ~ t o r q u e w i t h a 10% system vo l tage drop w i l l d e l i v e r 160% x (100%-10%) o r 129.6% torque t o i t s ou tput sha f t .

100

when, i t i s n o t poss ib le o r p r a c t i c a l t o s t a r t a f u l l y loaded synchronous motor across- the- l ine i t i s poss ib le t o u t i l i z e the motor,'^ p u l l - o u t torque t o s t a r t the m i l l . By us ing a c lu t ch , normal ly an a i r c l u t ch , between the motor and the m i l 1, the motor i s brought up t o synchronous speed before the c l u t c h i s energized. I f the motor has an adequate amount (175 o r g reater ) o f p u l l - o u t torque the p u l l - o u t torque s t a r t s the m i l l w i t hou t major d i s rup t i ons on the e l e c t r i c a l system.

Since the energy re lease a t i n i t i a l cascade o f the m i l l ' charge is . an i nve rse func t ion of acce le ra t i on time, a minimum acce le ra t i on t ime o f 6 t o 10 seconds o r more i s recommended t o prevent damage t o t he m i l l o r t he m i l l foundat ion.

Economics a t t he t ime o f p l a n t design and m i l l purchase determine the d r i v e t o be used. The s i m p l i e s t d r i v e i s the low speed synchronous motor w i t h speeds i n the range o f 150 t o 250 RPM connected t o the m i l l p i n i o n s h a f t by e i t h e r an a i r c l u t c h o r f l e x i b l e coupl ing. Using a speed reducer between the motor and p in ionsha f t permits us ing motors having speeds i n t he range o f 600 t o 1000 RPM. I n t h i s speed range, i f power f a c t o r c o r r e c t i o n i s n o t requ i red i nduc t i on motors can be used; s q u i r r e l cage where the re i s no r e s t r i c t i o n on in rush cur rent ; s l i p r i n g where a slow s t a r t and low in rush cu r ren t i s requ i red . A i r c lu tches can a l so be used t o ease s t a r t i n g problems w i t h s q u i r r e l cage motors. I n some areas o f t he wor ld i nduc t i on motors and s t a r t e r s a re l e s s expensive than synchronous motors a t a s a c r i f i c e o f motor e f f i - c iency and power f a c t o r co r rec t i on .

Dual d r ives , t h a t i s two p in ions d r i v i n g one gear mounted on the m i l l , become economical f o r ba.11 m i l 1 s drawing more than 3500 t o 4000 horsepower (2600 t o 3000 k i 1 owatts) . Fur ther developments o f the 1 ow frequency , low speed synchronous motors w i t h the r o t o r mounted on the m i l 1 she1 1 o r an extension o f one o f t he m i l l t runn ions cou ld improve the cos t p i c t u r e f o r these "gear less d r i ves " , making them p r a c t i c a l f o r l a r g e b a l l m i l l s .

The percent o f c r i t i c a l speed, which i s the speed a t which the c e n t r i - fuga l f o r ce i s s u f f i c i e n t l y l a r g e t o cause a small p a r t i c l e t o adhere t o t he s h e l l l i n e r s f o r the f u l l r e v o l u t i o n of. the m i l l i s g iven i n m i l 1 spec i f i ca t i ons . C r i t i c a l speed i s determined ' f rom the fo l l ow ing :

ROD AND BALL MILLS

Where D i s mill diameter inside l iners .specified in meters. Cs i s c r i t i c a l speed in RPM.

When D i s specified in fee t :

m -

Peripheral speed, which doesn't influence mill power but i s a factor in 1 iner wear and t o an extent media wear, has to be considered in mill design. I t can be determined by the following e i ther as meters per minute or as f ee t per minute.

where

Mp = Peripheral speed. D = Diameter inside l iners . N = Mill speed in rpm.

To obtain some balance of c r i t i c a l speed and peripheral speed as mill diameters increase, the average recomnended speed as percent of c r i t i - cal speed reduces as shown in Table I . These are guide l ines for in i - t i a l plant design. Actual speeds may d i f f e r from these to su i te speci- f i c ore and economic conditions tha t apply t o the, specif ic plant.

ROD 'MILLS

To prevent most kondi t ions leading t o rod charge tang1 ing, the general- ly recommended relationship of rod length t o mill diameter inside l i - ners i s 1.4 t o 1.6. When th i s ra t io becomes less than 1.25 the r i sk of tangling increases rapidly. For rod mills larger than 3.8 meters (12.5 f ee t ) in diameter rod ava i lab i l i ty and quality have t o be considered. Table I1 gives rod length to mill diameter ra t ios for the larger diameter rod mil ls .

6.8 meters (20 f e e t ) i s a practical l imit on the length of good qual- i t y rods ( t ha t i s rods that will stay s t raight in the mill and will . break into pieces tha t will discharge from the mill when worn). This length i s a function of rod quality and production l imi t s imposed by the suppliers. The mill length inside end l iners measured along the surface of the she1 1 l iners should be 0.1 t o 0.15 meters (4" to 6") longer than the rods, so that the rods will f i t in the length of the grinding chamber without tipping or laying across the charge. A slope as steep as possible should be used for rod mil 1 head (end) 1 iners to Prevent unsupported ends of rods from protruding from the charge and being broken under impact from other rods.

MINERAL PROCESSING PLANT.DESIGN

TABLE I

AVERAGE % OF CRITICAL SPEED . -

MILL DIAMETER % OF CRITICAL SPEED INSIDE LINERS

METERS FEET --- ROD MILLS BALL MILLS

0.91-1.83 3-6 76-73 80-78 1.83-2.74 6-9 . 73-70 78-75 2.74-3.66 9-12 70-67 75-72 . 3.66-4.57 12-15 67-64 72-69 4.57-5.49 15-18 69-66

TABLE I1 . . . .

ROD MILL DIAMETER - ROD LENGTH

MILL DIAMETER INSIDE LINERS

METERS FEET - -

3.81 12.5 3.96 13 4.11 13.5 4.27 14 4.42 14.5 4.57 15 4.72 15.5 4.88 ' 16 5.03 16.5

ROD LENGTH , L = 1.25 D L = 1 . 4 D -

I

- -

I METERS FEET METE'RS .FEET

ROD AND BALL MILLS , . I 245

The r o d s p e c i f i c a t i o n s given i n Table I 1 1 can be considered as a m in i - mum s p e c i f i c a t i o n . B e t t e r rod q u a l i t y , which reduces breakage, a l lows wearing the rods t o a smal ler s i z e and which can reduce rod opera t ing cos ts are ava i l ab le . The b e t t e r q u a l i t y rods are gene ra l l y recommended when us ing 100 mm ( 4 " ) diameter. rods and/or the l a r g e r .d iameter r o d m i l l s .

The feed end o f rods wear i n t o a long tapered "spear-shaped" p r o f i l e , w h i l e t he discharge ends wear i n t o more o f a con ica l shape. Approxi- mately the middle two t h i r d s o f the rod l eng th even tua l l y wears i n t o an e l i p t i c a l shaped sect ion. Small pieces o f broken rods can accumu- l a t e i n t he m i l l be fore being discharged. The tapered wear and accum- u l a t i o n o f broken rods reduces the bu lk dens i t y o f the m i l l charge, and thus m i l l power. The rod charge bu lk dens i t y g iven i n Table I V can be used t o determine the power a r o d m i l l w i t h a worn-in charge should draw. Bulk dens i t y i s a v a r i a b l e sub jec t t o care given a rod charge, and experience i nd i ca tes m i l l diameter a l so has an e f f e c t on b u l k dens i t y o f t he worn- in charge. The l a r g e r t h e diameter o f t he rod m i l l the l e s s p r a c t i c a l " c u l l i n g " o f the charge becomes.

Rod m i l 1 s normal ly c a r r y from a 35 t o 40% by m i 11 volume rod charge, they can c a r r y up t o a 45% charge. The l i m i t s on charge l e v e l are: keeping the feed end t runn ion open so feed w i l l go i n t o m i l l , and keeping the rod 'charge low enough so rods w i l l n o t work i n t o d ischarge end t runn ion opening, where they can t i p and cause rod tang l ing .

Rod m i l l s a re normal ly fed by spout feeders as shown i n Fig. 4. A minimum head o f 1.5 meters (5 f e e t ) above the m i l l center l i n e t o the bottom o f t he feed hopper t o which the feeder i s at tached i s requ i red t o g e t t h e proper f l o w o f feed i n t o the m i l l .

Heavy du ty s i n g l e wave she1 1 1 i n e r s cas t o f ' e i t h e r 'a1 l o y s tee l (manganese s tee l i s n o t recommended). o r . wear r e s i s t a n t a1 loyed cas t i r o n . are most f requent ly u s e d ' i n rod m i l 1s. The number o f l i f t e r s t o the c i r c l e i s u s u a l l y equal t o approximately 6.6 D - i n meters ( f o r D i n f e e t d i v i d e 6.6 D by 3.3). These l i n e r s have 65 (2.5") t o 90 nnn (3.5") h igh waves above 65 mm t o 75 mm ('3") l i n e r s . Rubber backing can be used between the l i n e r s and s h e l l ' . t o p r o t e c t the s h e l l from washing and cor ros ion . However, w i t h rubber backing care must be taken w i t h the l i n e r b o l t spec i f i ca t i ons , and sea ler assembly t o assure the l i n e r s w i l l s tay t i g h t and n o t move on. t he s h e l l . Th is creates leaky l i n e r b o l t s and causes the b o l t ho les i n t he s h e l l t o wear i n t o an elongated shape. There are modi f i ca t ions such as the two piece 1 i n e r - l i f t e r design t h a t can be used ins tead o f the s i n g l e wave l i n e r . Rubber s h e l l l i n e r s have been successful ly app l i ed i n the smal le r diameter rod m i l l s running a t slow speeds. When us ing rubber l i n e r s care must be given t o us ing good q u a l i t y rods and c u l l i n g broken and t h i n rods f rom the charge. Rubber l i n e r s can he lp reduce the no i se l e v e l emanating f rom a rod m i l l .


TABLE I1 I

MINIMUM ROD SPECIFICATIONS

Grinding ~ n i l l rods should be hard enough t o remain s t r a igh t throughout t h e i r e n t i r e l i f e , ye t they cannot be so b r i t t l e a s - t o break up a t coaise s i ze s .

When rods a r e too s o f t , they a r e subject to bending in the mi l l . Bending causes premature breakage and tanglement of rods. Tangled rods make mil 1 cleaning d i f f i c u l t and hazardous, and cause cos t ly downtime.

Material of the following chemical analysis i s recommended :

CHEMICAL ANALYSIS

Carbon 0.85 t o 1.03%

Manganese 0.60 t o 0.90%

Si l icon 0.15 t o 0.30%

Sulphur 0.05% Max.

Phosphorous 0.04% Max.

PHYSICAL REQUIREMENTS Rods should a l so have the following physical requirements:

. Rods a re t o be special commercial straightened.

. Rods a re t o be hot sawed to length where mill ( s t e e l ) f a c i l i t i e s permit. If hot sawing i s not possible, use amabrasive cut t ing wheel o r machine cu t both ends t o proper length.

. All grinding mill rods should be 152 mn (6 inches) shor ter in length than the working length of t he rod mill .

ROD AND BALL MTLLS 247

TABLE I V

BULK DENSITY WORN-IN ROD CHARGES

BULK DENSITY KG PER CUBIC METER LBS PER CUBIC FOOT

NEW RODS 6 2 4 7 3 9 0

WORN-IN CHARGE

M I L L DIAMETER

METER FEET

F i g . 4 - Spout Feeder


End l i n e r s a re gene ra l l y a t h i ck , smooth l i n e r cas t o f a l l o y s tee l . Impact ing f rom the r o d charge, which has a l a t e r a l movement i n t h e m i l l , r equ i res g rea t cau t i on i n us ing wear r e s i s t a n t cas t i r o n end liners. Rubber l i n e r s can be used w i t h caut ion as they can be sub jec t t o damage from the sharp ends on worn rods. Except when us ing rubber l i n e r s t he re should be a rubber backing between the head l i n e r s and the heads. End l i n e r s should be smooth w i t h no waves o r . l i f t e r s as these can d i s r u p t rod a c t i o n and cause rod tang l i ng .

Rod m i l l s can be equipped w i t h trommels t o remove bioken pieces of rods and tramp overs ize from the rod m i l 1 discharge. The discharge end o f a r o d m i l l can be enclosed i n a housing which w i l l he lp con- t a i n t he no ise and splash coming from the m i l l . A door should be pro- v ided a t the end o f the housing which can be opened f o r charging rods. S u f f i c i e n t c l e a r space a t the discharge end o f the m i l l should be a l - lowed f o r charging rods. See F ig . 5.

The f o l l o w i n g equat ion i s used t o determine the power t h a t a .rod m i l l should draw.

where

K W ~ = K i l owa t t s per m e t r i c tonne o f rods (1000 kg). D = M i l l diameter i n s i d e l i n e r s i n meters. V = F r a c t i o n 'of m i l l volume loaded w i t h rods. fbs = F rac t i on o f c r i t i c a l speed.

I n terms o f m i l l diameter i n fee t and rod charge i n sho r t tons (2000 pounds) t h e equat ion becomes:

Table V l i s t s many o f t he common s i z e rod m i l l s g i v i n g speed, l oad ing and power data. The power i s i n horsepower a t the m i l l p i n ionsha f t . For d i f f e r e n t l eng th rod m i l l s power va r i es d i r e c t l y as rod length . For d i f f e r e n c e between new and worn l i n e r s increase power draw by 6%, and a d j u s t f o r bu l k dens i t y per Table I V . Wet g r i n d i n g rod m i l 1s a r e normal ly used. i 'n minerals processing p lan ts . Experience w i t h d r y g r i n d i n g genera l ly i nd i ca tes many d i f f i c u l t problems and should be avoided except where abso lu te l y necessary; i n which case the problem should be re fe r red t o the m i l l manufacturers f o r r e - comnendations.

The var ious rod m i l l manufacturers have d i f f e r e n t equat ions f o r de te r - min ing t h e power rod mi 11 s draw, bu t a1 1 come c lose t o the same ca lcu- l a t e d power draw.

ROD AND BALL MILLS

249

TABLE V

ROO M I L L POWER AT M I L L PINIONSHAFT (HORSEPOWER)

ROO 'ROO MILL M I L L DIAMETER LENGTH

-.

' ROD AND BALL MILLS . 251

BALL MILLS

Being f ree o f t he 1 i m i t s imposed on rod m i l 1s by the rods, b a l l m i l 1 s have more v a r i a t i o n s i n l eng th t o diameter r a t i o s , ranging from LID r a t i o s o f s l i g h t l y l e s s than 1 :1 t o some greater than 2: l . There are no f i x e d r u l e s on the proper LID r a t i o s t o use as these vary w i t h the c i r c u i t used, o re type, feed s i z e and o v e r a l l g r i nd ing requirements.

. Table V I g ives some rough guide 1 ines showing, based upon past exper i - ence, the general C /D r a t i o s used i n the a p p l i c a t i o n o f b a l l m i l l s .

Gr ind ing b a l l s can be made o f fo rged o r cas t s tee l o r cas t i r on . The q u a l i t y depends upon the source o f supply. While n o t always t rue , f r equen t l y the b e t t e r qua1 i t y b a l l s a re forged s tee l . General 1 y b a l l s a r e spher ica l shaped, b u t they can be i n var ious c y l i n d r i c a l , con ica l o r o the r i r r e g u l a r shapes. B a l l s vary considerably i n hardness w i t h s o f t b a l l s having B r i n n e l l hardnesses i n the range o f 350 t o 450, and t h e hard b a l l s having hardnesses i n excess o f 700. A r u l e o f thumb sub jec t t o arguments i s : " t he harder t he b a l l the b e t t e r i t s l i f e " (provided i t i s n o t too b r i t t l e and breaks 'or becomes too h i g h l y po l - ished and too smooth t o n i p the ma te r i a l being ground). .Local economics and the s p e c i f i c g r i nd ing a p p l i c a t i o n genera l ly a re the dec id ing f a c t o r s i n s e l e c t i n g the b a l l s t o use. The b a l l s g i v i n g the lowest opera t ing cos t and best performance are genera l ly selected. This need n o t be the lowest p r i c e d b a l l s a v a i l a b l e nor the ones g i v i n g the 1 owest wear ra te , b u t can 'be a compromise between the two extremes.

B a l l s should -be s o l i d w i t h a reasonably un i fo rm hardness t h r u the en- t i r e b a l l . They should wear i n a r e l a t i v e l y un i fo rm pat te rn . An i n - d i c a t o r o f good b a l l wear i s when the worn b a l l s d ischarg ing from the m i l l a re around 16 m i l l i m e t e r ( 518 " ) o r smal ler i n s i z e and a re po ly - gon shaped having as many as 8 t o 12 surfaces, which can be s l i g h t l y concave. Evidence o f broken b a l l s i s found when pieces o f b a l l s a re being discharged, some as c i r c u l a r d iscs, some as h a l f rounds, some ' crescent shaped. Pieces o f worn o r broken b a l l s w i t h holes i n them ' i n d i c a t e poor q u a l i t y b a l l s w i t h sand i nc lus ions and/or blow holes and/or ho l low centers.

For c a l c u l a t i n g the power t h a t a b a l l m i l l w i l l draw, forged s tee l and cas t s tee l b a l l s a re assumed t o weigh 4646 ki lograms per cubic meter (290 pounds e r cub ic f o o t ) w i t h cas t i r o n b a l l s weighing 4165 kg per m3 (260 p c f r . B a l l mi 11 s normal ly c a r r y a b a l l charge 'occupying from 40 t o 45% o f t he m i l l volume, b u t can c a r r y up t o a 50% o r s l i g h t l y h igher charge. F ig . 6 shows the r e l a t i o n s h i p o f m i l l power and vo lumet r ic loading. For p l a n t capac i ty and design purposes, b a l l m i l l s a re f requen t l y se- l e c t e d based upon ca r r y ing 40% b a l l charges w i t h the m i l l s and d r i ves designed t o c a r r y h igher charges i f required.

252 MINERAL PROCESSING PLANT DESIGN TABLE V I

B A L L M I L L L / D R A T I O - APPLICAT.ION' GENERAL GUIDEL INES

,, . . . . .

. ,

FEED 8 0 % PASSING S I Z E . . . TOP. BALL S I Z E LID ,RATIO ' :: , . .

- . MICROMETERS ' MILLIMETER INCHES . . .

, ,

2 % OF MlLL VOLUME OCCUPIED BY BALL OR PEBBLE CHARGE GRINDING MlLL POWER VS LOADING Fig . 6

. . ROD. AND -BALL. *MILLS . 253

When a 45 t o 50% b a l l charge i s t o be ca r r i ed , gene ra l l y a double scoop feeder as shown i n Fig. 7 i s used. Th is i s a more expensive feeder than a spout feeder. as shown i n F ig . 4 , which can a l s o be used t o feed b a l l m i l l s . P l a n t design, c a p i t a l cos t and opera t ing cos ts a l l i n f l uence b a l l m i l l feeder se lec t ion . When a b a l l m i l l i s c losed c i r c u i t e d w i t h a rake o r s p i r a l c l a s s i f i e r , a scoop feeder i s requ i red t o feed the c i r c u l a t i n g l oad i n t o the m i l l . With cyclone c l a s s i f i e r s spout feeders can be used. Spout feeders a l l ow arrangement where the c l a s s i f i e r underf low f lows by g r a v i t y i n t o t he spout feeder hopper. Therefore, the cyclone c l a s s i f i e r s must be i n s t a l l e d h igh enough t o o b t a i n t he head requ i red f o r t h i s f l o w i n t o the hopper. This can r e - s u l t i n h igh pumping heads and pump power t o pump the m i l l discharge t o t he cyclone c l a s s i f i e r s . F ig . 8 shows a s i n g l e stage b a l l m i l l i n - s t a l l a t i o n us ing double scoop feeders w i t h cyclone c l a s s i f i e r s i n s t a l - l e d a t about t h e ho r i zon ta l c e n t e r l i n e o f the m i l l . Depending upon t h e rad ius and w id th o f t he scoops and the c a p a ~ i ~ t y ( i n c l u d i n g c i r c u - l a t i n g load) double scoop feeders consume from 25 t o 30 k i l o w a t t s (20 t o 40 horsepower). Th is arrangement reduces considerably pumping head and power and must be balanced aga ins t h igher maintenance cos t f o r the scoop feeder.

Make-up g r i nd ing b a l l s a re fed t o the m i l l as requ i red t h r u the m i l l feeder w i t h the m i l l i n operat ion. B a l l s may feed d i r e c t l y through a spout, b u t should not be fed i n t o a scoop box because o f poss ib le jamming and ser ious mi 11 damage. Scoops usual 1 y have a. cen t ra l b a l l feed p ipe o r a small charging drum t o accomplish t h i s .

. :

There a re many d i f f e r e n t designs and s t y l e s o f b a l l m i l l l i n e r s . As w i t h ' g r i n d i n g b a l l s l o c a l economics and u l t i m a t e l y opera t ing costs determine. the. best ' design and ma te r i a l t o use. The i n i t i a l s e t o f 1 i n e r s ' is , r a re l y t h e f i n a l design, selected. Based upon i n d i v i d u a l experience-, mil.1 superintendents develop perferences f o r l i n e r de- s igns. 'The:following i s g iven as a guide l i n e f o r the i n i t i a l s e t o f 1 i ne r i ' ;

4 . . . 7 . ' . .. ' .

A. - ~ d r 60 mm ' ( 2 . 5 " ) and smal.ler t i p - i i z e . b a l l s f o r cas t metal ; 1.i'ners use double wave 1 iners.:wi t h the number o f l i f t e r s t o " t he c i r c l e approximately 13.1 D i n meters ( f o r D i s i n f e e t

. d i v i d e 13; 1 D by 3:3). Wave he ight above the 1 i n e r s from 1.5 t o 2 'times the l i n e r th ickness. Rubber l i n e r s o f t he i n t e g r a l .molded design f o l l o w the cas t metal design. I f us ing the' replaceable l i f t e r bar design i n e i t h e r metal o r rubber t he number o f l i f t e r s should be about 3 . 3 T D i n

, meters ( f o r D i s i n f e e t d i v i d e 3.3-fD by 3,3) w i t h the '

. . l i f t e r he igh t above the l i n e r s about tw ice the l i n e r t h i c k - ness. ...' . . . . .

. . . .

. The use o f double wave. 1 iners , p a r t i c u l a r l y 'when using 5 6 inm (2 " ) . o r l a r g e r bal.ls, may show a l oss of 5% o r so i n the

- - ' m i l 1 power draw u n t i l the waves wear i n 'and' the b a l l s can


F i g . 7 - S i n g l e o r Double Scoop Feeder

F i g . 8 - Duval S i e r r i t a P l a n t

ROD AND BALL MILLS

nes t between the l i f t e r s . When l i n e r s , and double wave liners i n particu1ar;wear w i t h c i r cumfe ren t i a l grooves, s l i p - p ing o f t he charge i s indicated, and t h i s warns o f accele- r a t e d wear. When the top s i ze b a l l i s smal ler than 60 mm (2.5") and m i l l speed i s l ess than 72% o f c r i t i c a l wear re- s i s t a n t cas t i r ons can be used. For o ther cond i t ions a l - loyed cas t s tee l i s recommended.

Rubber 1 i n e r s are we l l su i ted t o t h i s same area and no t on l y reduce operat ing costs b u t can reduce no ise l e v e l s .

B. S ing le wave l i n e r s are recommended f o r l a r g e r s i z e b a l l s (60 mm/2.5" and l a rge r ) . The number o f the 1 i f t e r s t o the c i r - c l e equals approximately 6.6 D i n meters ( f o r D i s i n f e e t d i v i d e 6 . 6 D b y 3.3). T h e l i n e r s a r e f r o m 5 0 t o 6 5 m m t h i c k (2" t o 2.5") w i t h the waves from 60 t o 75 mm (2.5" t o 3") above the 1 iners . The replaceable l i f t e r bar design made o f e i t h e r metal o r rubber i n about t he same design propor- t i o n s can be used. There could be a l oss i n power w i t h rubber p a r t i c u l a r l y i f the m i l l speed i s f a s t e r than about 72% o f c r i t i c a l speed and the b a l l s i ze i s l a r g e r than 75 mm .

Because o f the impacting from the l a rge ba l l s , s i ng le wave 1 i n e r s f o r b a l l m i l l s are usua l l y made from a1 loyed s tee l s o r special wear-resistant a l l oyed cas t i rons. Because o f t he d i f f i c u l t y o f , balancing growth and wear w i t h work hard- ening manganese s tee l i s used in f requen t l y and then w i t h ex- treme care t o a l l ow f o r growth.

C. End l i n e r s f o r b a l l m i l l s c o n f o r m t o t h e s l o p e o f t h e m i l l head and can be made o f rubber, a l loyed cas t s tee l o r wear resistant . , cas t i r on . To prevent rac ing and excessive wear

. end 1 i n e r s . f o r ' b a l l m i l l s are furn ished w i t h i n t e g r a l r a d i a l r i b s o r w i t h replaceable l i f t e r s o r w i t h both.

D. When a g ra te discharge i s used the grates and wear p la tes are normal ly perpendicular t o the m i l l ax i s wh i l e the d i s - charge pans conform t o the slope o f the m i l l head. The gra tes and wear p la tes are normal ly made from a l loyed wear r e s i s t a n t cas t s tee l o r rubber. They are r ibbed t o prevent r a c i n g and excessive wear. The dischargers and pans a re genera l l y made from e i t h e r wear r e s i s t a n t cas t i r o n o r rubber, o r wear r e s i s t a n t f ab r i ca ted s tee l .

S l o t p lugg ing can be a problem i n gra te discharge m i l l s . Whether the grates are made o f metal o r rubber the s l o t s should have ample r e l i e f tapered toward t h e discharge side. Tota l angles 7 t o 10 degrees (3.5 t o 5 degrees per s ide) are commonly used. Metal grates o f t e n have


' ' ' . a small lead-i.n 'po,cket o r reces's whi'ih 'can f i 1.1 i n w i t h -. peened meta1"rather than have the * s l o t peen: shut.' With

the proper combinati.on o f metal, i - n t h a l s and r l jbber surfaces,' rubber gra tes ' .have" f lex ' ib i l i ty t h a t tend' to make them se l f c leaning and y e t no t f a i l due t o f l e x i n g .

. ..

E. Except when using rubber l i n e r s , the m i l l surfaces are covered w i t h a p r o t e c t i v e rubber o r p l a s t i c ma te r ia l t o p r o t e c t the surfaces from pu lp rac ing and corrosion. Th is i s done i n wet g r i nd ing m i l l s : Since d ry g r i nd ing m i l l s ge t ho t due t o heat from g r ind ing genera l ly rubber l i n e r s and rubber ma te r ia l s cannot be used.

\ >

The follow in^ equation.'i's used t o determine the power t h a t wet g r i nd - i n g overf low ba1.l m i l 1 s- should draw.

. .

= 1.879 (3.2-3 vp) .+ :

. . . .

where . -. . . .

K W ~ = K i l owa t t s per me t r i c tonne o f b a l l s (1000 kg) . D = M i l l diameter i n s i d e l i n e r s i n meters. V = F rac t i on o f m i l l volume loaded w i t h b a l l s . fFs = F rac t i on o f c r i t i c a l speed.

I : Ss = B a l l s i ze factor.. . .

I n terms o f m i l l diameter i n fee t ' and power'per sho r t t on a t (2000 pounds) o f b a l l charge Equation 4 becomes:

For m i l l s l a r g e r than'. 3.3 meters. (10 f e e t ) d iameter" inside' l i n e r s the top s i z e o f t he b a l l s used a f f e c t s the power,drawn by. the niill. This

. . . . i s c a l l e d the b a l l s i ze f a c t o r S,. . . .-.L i . '

where

B = B a l l s i z e i n m i l l i m e t e r s . * ,- D '= M i l l diameter i n s i d e l i n e r s i n meters: ' - 1 Ss = K i l owa t t s per me t r i c tonne o f ba l l s .

I n terms o f b a l l s i ze i n inches and m i l l diameter i n f e e t and power per sho r t t on of b a l l charge equation 5 becomes: ;

- ROD AND' BALL MILLS . , 257

To determine the power t h a t a wet gr inding, low l e v e l g ra te discharge m i l l should draw m u l t i p l y Kwb by 1'.16 +and f o r a d ry gr ind ing, f u l l g ra te discharge m i l l m u l t i p l y by 1.08. .

For spec ia l app l i ca t i ons :such as cement raw.mater ia ls, baux i te i n cau- s t i c so lu t i ons and 'other. ,c lay- l i ke mater ia ls consu l t the m i l l manufac- t u re rs , s ince . these, mat,erial s a f f e c t the power drawn by b a l l mi 11 s.

. . . . ' , : , :; - . .

Table V I I 1 ists,' e i s e n t i a l l y "square" b a l l m i l l s g i v i n g h i 1 1 speed as percent o f cri-t.ica.1, 'weight o f a '40% b a l l charge, t o p b a l l s i ze and ca l cu la ted power .draw. B a l l m i l l power chan'ges i n d i r e c t propor t ion t o m i l l length:.' The power is horsepower a t ' the m i l 1 p i ,n ionshaft i n - s ide new s h e l l . l i 'ners. Increase power f o r worn.-shell. l i n e r s by 6%. There are i nd i ca t i ons ' t h a t ,rubber 1 i ne rs ' may cause: from a 5 t o 10%

. . . . - -

. . l o s s i n m i l 1 power. : . .

. .

7 :_ : . , , , . - . . . . . . . . 2 .

. .

. .

The var ious. bd-l:l'-.mi'll man"facturers have : d i f f e r e n t equtitions f o r deter - mining the power ,ba.ll m i l l s draw, ,but a l l come close t o the same calcu-

. . . l a t e d power'draw. - . .

. . , .

. , .

, , . 1.;. O R E TESTING FOR MILL-SELECTION ~.

A f t e r the g r i nd requirements are establ ished, t e s t i n g f o r the selec- t i o n o f comminution c i r c u i t s and m i l l s i ze can-be i n i t i a t e d and can inc lude the fo l lowing:

- Primary ~ u t o ~ e n o u s Media Competency - Primary Autogenous and Semi-Autogenous P i l o t P lant - Secondary Autogenous (Pebble) Test ing - Impact Crushing - Bond Work Index - Rod M i l 1 Grindabi li t y - Bond Work Index - B a l l M i l l G r i n d a b i l i t y - Bond Work Index - Abrasion Index . - Crushing, Gr inding and Concentration P i l o t P lant

Th is discussion w i l l be 1 im i ted t o t e s t i n g f o r se lec t i on o f rod and b a l l m i l l s . Rod and b a l l mil l . ing, using g r i nd ing media o f known qual- i t y , a re we l l es tab l ished and requ i re much s imp l i e r g r i nd ing t e s t programs than requ i red f o r t he se lec t i on o f autogenous g r ind ing mi 11s and c i r c u i t s . - . .

Samples f o r g r i n d a b i l i t y tes ts -shou ld be crushed. t o ab&t minus 1". The samples can',be taken from ad i ts , p i t s , etc., ' i n the ore body o r they can be crushed d r i q l cores.. . While i t i s he lp fu l i n a n t i c i p a t i n g va r ia t i ons i n - feed. ra tes . t o know the g r i ndab i l i t y o f t he var ious ore types i n a deposit, f o r m i l l se lec t i on g r i n d a b i l i t y t e s t s should be run on composite samples representa t ive -o f t he blended m i l 1 feed. It i s in f requent t h a t the. g r i n d a b i l i t y o f the. composite or , b lend i s the same as t h a t obta'iried by mathenia+jcal l y maki ng'.a propor t iona l blend based on gr indab' i l . . . . . i t y t e s t s performed bn each: component. D i f f e r e n t i a l

TABLE VII

BALL M I L L POWER AT M I L L PINIONSHAFT (HORSEPOWCR)

M I L L

ROD AND BALL MILLS 259

g r i n d i n g occurs so t h a t each component can be ground t o a d i f f e r e n t s i z e c o n s i s t than the composite which has been ground t o t he requ i red s ize .

Depending upon the s i z e o f the deposi t , capac i ty o f the concentrator , l i f e o f the operat ion, complexi ty o f the ore deposi t , complexi ty o f t he e x t r a c t i o n o r subsequent processes, etc., t e s t i n g can range from one se r i es o f g r i n d a b i l i t y t e s t s t o a l a r g e number o f g r i n d a b i l i t y t e s t s and even poss ib l y p i l o t p l a n t t e s t i n g . Often p i l o t p l a n t t e s t - i n g i s done p r i m a r i l y f o r m e t a l l u r i g i c a l t e s t i n g w i t h g r i nd ing used f o r feed preparat ion.

Frequent ly p i l o t p l a n t s a re b u i l t us ing ava i l ab le o r used equipment w i t h t he g r i n d i n g c i r c u i t overs ize f o r the concent ra t ion sec t i on and as such the two are n o t balanced operat ions. Caution, there fore , should be used i n s e l e c t i n g the t e s t data t o be used t o s e l e c t m i l l s and c i r c u i t s f o r t he p lan t . The data should be selected from t e s t s run s p e c i f i c a l l y t o ob ta in g r i nd ing data. This data should inc lude:

M i l l S ize % vo lumet r ic load ing i n m i l l occupied by media. Type o f c i r c u i t (open o r c losed) and f lowsheet diagram. Any concent ra t ion steps i n the g r i nd ing c i r c u i t . S ize and type o f c l a s s i f i e r s . I f cyclone c l a s s i f i e r s : s ize, ra ted capacity, power

draw and speed o f cyclone feed pump. S ize ana l ys i s c i r c u i t feed. , % mois ture i n m i l l feed. Feed r a t e t o the c i r c u i t , d r y basis. S ize ana l ys i s and pu lp dens i t y of:

1.) C i r c u i t product. 2.) Discharge f rom each m i l l . 3 . ) Feed t o each c l a s s i f i c a t i o n stage. 4.) Oversize from each c l a s s i f i c a t i o n stage. 5.) Fines from each c l a s s i f i c a t i o n stage.

Power drawn by each m i l l (motor i n p u t ) . Motor and d r i v e e f f i c i e n c y o f each m i l l . S ize o f and type o f g r i n d i n g media used i n

each mi 11. Speed i n rpm f o r each m i 11 . L i n e r design and c o n d i t i o n i n each m i l l .

.Media wear ra te . L i n e r wear r a t e i f tes ted l ong enough t o

obta in . % c i r c u l a t i n g l oad f o r each stage t h a t

i s c lose c i r c u i t e d .

During g r i q d i n g t e s t s obtain"samp1es o f m i l l feed f o r g r i n d a b i l i t y t e s t s so t h a t work i nd i ces ' ca l cu la ted f rom the p i l o t p l a n t data can be compared t o gr indab i 1 i t y t e s t r e s u l t s . Operating work ind ices


can be o b t a i n e d u s i n g p i l o t p l a n t d a t a i n t h e f o l l o w i n g equa t ion :

where.

wio = Opera t ing Work Index. W = Kwh p e r t o n (can be m e t r i c , s tandard o r l o n g ) . P = Produc t s i z e which 80% passes i n micrometers. F = Feed s i z e which 80% passes i n micrometers.

The a p p l i c a t i o n o f g r i n d i n g c i r c u i t and equ ipment - re la ted f a c t o r s d i s - cussed l a t e r i n t h i s c h a p t e r a r e a p p l i e d t o Wio t o p u t i t on t h e same b a s i s a s g r i n d a b i l i t y t e s t r e s u l t s . T h i s a l l o w s a d i r e c t compar ison o f p i l o t p l a n t t e s t r e s u l t s and g r i n d a b i l i t y t e s t r e s u l t s . I n a d d i - t i o n t o these, a1 so, be s u r e t o a p p l y motor and ' d r i v e e f f i c i e n c y f a c - t o r s so t h a t t h e p i l o t p l a n t m i l l power d a t a i s r e f e r e d t o t h e m i l l p i n i o n s h a f t o r t o t h e m i l l s h e l l (measured power d a t a . i s g e n e r a l l y e l e c t r i c a l energy i n t o t h e moto r ) . F o r comparison w i t h g r i n d a b i l i t y t e s t r e s u l t s Wio has t o be p laced on t h e b a s i s o f s tandard t o n s (907.4 kg) - W i t h t h e d i f f i c u l t y i n o b t a i n i n g a c c u r a t e p i l o t p l a n t da ta , p a r t i c u - 1 a r l y power data, Bond c l o s e d c i r c u i t g r i n d a b i li t y t e s t r e s u l t s o f t e n g i v e t h e more a c c u r a t e d a t a f o r s e l e c t i n g r o d and b a l l m i l l s . Gr ind - a b i l i t y t e s t work shou ld span t h e f e e d and p r o d u c t s i z e s of t h e p ro - posed g r i n d i n g c i r c u i t . The g r i n d a b i l i t y t e s t work g e n e r a l l y recommended f o r p r i m a r y m i l 1 i n g c i r c u i t s . i nc ludes :

A. Bond r o d m i l l g r i n d a b i l i t y t e s t s a t 10 o r 14 mesh f o r Work Index .

B; F o r each b a l l m i l l g r i n d i n g s tep, a Bond b a l l m i l l g r i n d - a b i l i t y t e s t f o r Work Index a t one mesh s i z e c o a r s e r t h a n t h e d e s i r e d 80% pass ing s i z e and a t t h e mesh s i z e o f o r j u s t f i n e r t h a n the. 80% pass ing s i z e .

C. I f 50 mm x 75 mm (2" x 3 " ) o r e .lumps a r e a v a i l a b l e an im- p a c t c r u s h i n g Work Index, t e s t . ' , ' .

D. I f 30 mm x 20 mm (1-114" x .314") o r e i s a v a i l a b l e an abra- s i o n index test . '

F o r r e g r i n d b a l l ' m i l 1 i n g o r b a l l m i l l i n g o f rougher concen t ra tes p ro - duced i n t h e g r i n d i n g c i r c u i t r u n b a l l m i l l g r i n d a b i l i t y t e s t s as o u t - 1 i n e d i n B above. S ince t h e Bond g r i n d a b i l i t y t e s t r e q u i r e s a r a t i o o f r e d u c t i o n of abou t 6 : l t o o b t a i n a c c u r a t e r e s u l t s i t may be neces- s a r y t o r u n t h e t e s t a t a f i n e r s i z e t h a n r e q u i r e d by t h e s p e c i f i e d


g r i n d o r even a spec ia l ' t e s t w i l l have t o be run. . ..

Th is w i l l g i v e a good cross sec t i on o f the g r i n d a b i l i t y o f t he o re and w i l l a l l o w f o r accurate ca l cu la t i ons o f the g r i nd ing power required.

The balance' o f the d iscuss ion i n the chapter w i l l be an example demon- s t r a t i n g the s e l e c t i o n o f a pr imary g r i nd ing c i r c u i t and a r e g r i n d c i r c u i t where a l l o f t he o re i s ground t o the requ i red product s i z e i n t he pr imary c i r c u i t . For g r i nd ing c i r c u i t s where concent ra t ion i s i n - c luded i n t he c i r c u i t the bas ic approach i s the same as given i n the example, cons ider ing each s t a e as a separate e n t i t y and ad jus t i ng f o r new feed r a t e s and feed s i r e ?which. could be d i f f e r e n t than the r a t e and product s i z e from the preceding stage).

PROBLEM .

Se lec t r o d m i l l s , b a l l m i l l s and pebble mi 11s as requ i red f o r the f o l - lowing c i r c u i t s .

- Rod M i l l - B a l l M i l l - S ing le Stage B a l l M i l l - Rod M i l l - Pebble (Secondary Autogenous) M i l l - Primary Autogenous o r Semi-Autogenous M i l 1 -' B a l l M i l 1. - Regrind B a l l M i 11

Feed r a t e t o the pr imary m i l l , c i r c u i t i s 500 me t r i c tonnes per hour i n c l u d i n g f a c t o r f o r a v a i l a b i l i t y . Feed r a t e t o r e g r i n d m i l l i s 40 me t r i c ' tonnes per hour.

Rod m i l l feed and feed f o r s i n g l e stage b a l l m i 11 w i l l be prepared w i t h c losed c i r c u i t crushing. The feed s izes f o r the var ious m i l l s -, w i l l be: . ,

- Rod M i l l i n g : minus 25 mm 80% passing 18 mm. S ing le stage B a l l M i l l : minus 12 mm 80% passing 9.4 mm.

- B a l l M i l l and Pebble M i l l f o l l o w i n g Rod M i l l and B a l l Mi 11 f o l l o w i n g Primary Autogenous o r Semi-Autogenous M i l l : minus 2 mm 80% passing 1.2 m.

- Regrind B a l l M i l l : 80% passing 210 micrometers.

The c i r c u i t s are a l l wet g r i n d i n g type. A l l b a l l o r pebble m i l l s are c losed c i r c u i t w i t h t he except ion o f the reg r i nd m i l l which w i l l be open c i r c u i t f o r t h i s example.

Pebble s i z e f o r pebble m i i l i n g p lus 30 mm minus 70 mm w i t h a pebble consumption o f 30 m e t r i c tonnes per hour which i s 6% o f the c i r c u i t p roduct ion r a t e .

, . ,

The spec i f i ed g r i nds are: pr imary g r i nd ing c i r c u i t 80% passing 175 micrometers, r e g r i n d c i r c u i t 80% passing .45 micrometers.

. .


Bench sca le g r i n d a b i l i t y t e s t r e s u l t s t o be used f o r g r i nd jng power ca l cu la t i ons . The t e s t r e s u l t s t o be used i n the example are:

Impact Crushing Work Index 11.5 Rod M i l l G r i n d a b i l i t y Test a t 10 mesh 13.2 ,(Mi) B a l l M i l l G r i n d a b i l i t y Test a t 65 mesh 11.7 .'(wi) B a l l M i l l G r i n d a b i l i t y Test a t 100 mesh 12.1 (Wi), B a l l M i l l G r i n d a b i l i t y Test a t 325 mesh

on r e g r i n d m i l l feed 14.0. (Mi) . Abrasion Index 0.215 ( A * ) ? :.

EQUATIONS USED TO DETERMINE GRINDING POWER.

Th is f i r s t s tep i n se lec t i ng g r i n d i n g m i l l s i s t o determine the power needed t o produce the des i red g r i nd . The bas ic equation used f o r t h i s i s the Bond Equation.

where

W = kwh per s h o r t ton. Wi = Work Index. P = Product s i z e i n microns which 80% passes. F = Feed s i z e i n microns'which 80% passes. , , .

I . . . . -

The power determined from equat ion 7 i s f o r the f o l l o w i n g spec i . f i c cond i t ions .

A. Rod M i l l i n g - wet, open c i r c u i t g r i nd ing i n a 2.44 meter ( 8 ' ) diameter i n s i d e l i n e r s rod m i l l .

B. B a l l M i l l i n g - w e t , c l o s e d c i r c u i t g r i n d i n g i n a 2.44meter ( 8 ' ) diameter i n s i d e l i n e r s b a l l m i l l .

C. Power ca l cu la ted i s t he power requ i red a t t he p i n i o n s h a f t o f the m i l l , which includes m i l l bearings and gear p i n i o n losses b u t does n o t i nc lude motor losses o r losses i n any o the r d r i v e component, such as reducers and c lu tches.

The feed f o r Bond G r i n d a b i l i t y Tests i s :

Rod m i l l i n g ore crushed t o minus 13,200 micrometers (0.530") o r f i n e r . B a l l m i l 1 i n g o re crushed t o minus 3,350 micrometers (6 mesh) o r f i n e r .

which have been used t o e s t a b l i s h optimum rod and b a l l m i l l feed s izes.

, ' ' ROD AND BALL MILLS 263

There a re e i g h t e f f i c iency fac tors t o be app l ied t o the ca l cu la ted g r i n d i n g power t o a l l ow f o r v a r i a t i o n s from the spec i f i ed cond i t ions and optimum feed s izes.

EF1 Dry, Gr.indi,ng': . .

EF2 Open C i r c u i t B a l l M i l l i n g .

EF3 Diameter . E f f i c i e n c y Factor.

EF4 Oversized Feed.

EF5 F ine Gr ind ing i n b a l l m i l l s t o product s izes f i n e r than 80% passing 200 mesh (75 micrometers).

EF6 High o r low r a t i o o f reduct ion rod m i l l i n g .

EF7 Low Ra t i o of reduc t i on b a l l m i l l i n g .

EF8 Rod M i l l i n g .

The m u l t i p l i e r s f o r the e f f i c i e n c y f a c t o r s are determined by the f o l - 1 owing:

EF1 - Dry Gr ind ing - f o r the same range o f 'work, d r y g r i nd ing r e - qu i res 1.3 t imes as much power as wet gr ind ing.

EF2 - Open C i r c u i t Gr ind ing - when g r i nd ing i n open c i r c u i t b a l l m i l l s , the amount of ex t ra power required, compared t o c losed c i r c u i t b a l l m i l l i n g , i s a func t ion o f the degree

. o f c o n t r o l r equ i red on the product produced. The i n e f f i - c iency f a c t o r s f o r open c i r c u i t g r i nd ing are given i n Table VIII.

EF3 -.Diameter E f f i c i ency Factor - using the base m i l l diameter o f 2.44 meters ( 8 ' ) i n s i d e l i n e r s , the diameter e f f i c i e n c y fac to r can be ca l cu la ted from the fol lowing:.

I '

When D i s i n meters:

When D i s

EF3 =

Table I X g ives a t abu la t i on ' o f the EF fac tors f o r some o f t he more common m i l l diameters i n bot; the imper ia l and m e t r i c measuring systems.

MINERAL PROCESSING PLANT DESIGN TABLE V I I I

. ..

OPEN CIRCUIT INEFFICIENCY MULTIPLIER

PRODUCT SIZE CONTROL REFERENCE % PASSING

INEFFICIENCY MULTIPLIER '

DIAMETER EFFICIENCY MULTIPLIERS

MILL DIAMETER MILL DIPJ~ETER DI'AMETER 'EFFICIENCY INSIDE SHELL. . INSIDE LINERS MULTIPLIER

FEET METERS , FEET METERS

3.0 0.914 2*.6 0.79 1.25 3.281 1.0 2.88 0.88 . 1.23 4.0 1.22 3.6 1.10 " . 1.17 5.0 1.52 4.6 1.40 ' 1.12 6.0 1.83 5.6 1.71 1.075 6.562 2.0 5.96 1.82

. .

1.06 7.0 2.13 6.5 1.98 1.042 8.0 2.44 7.5 2.29 1.014 8.5 2.59 8.0 2.44 . 1.000 Base 9.0 2.74 8 . 5 0

It ' should be noted t h a t f o r m i l l s where the diameter i ns i de l i n e r s i s l a r g e r than 3.81 meters (12.5 ' ) t h a t the.diameter e f f i c i e n c y f a c t o r does n o t change and remains 0.914.


NOTE: I n s e l e c t i n g m i l l s f o r new operations, where t h i s f a c t o r i s , l ess than 1.0 i t i s sometimes neglected and i s used as a

sa fe t y f a c t o r . I n the example i t w i l l be appl ied.

EF4 -. Oversized Feed - when being fed a coarser than optimum feed, t h i s f a c t o r app l i es t o r o d . m i l l i n g and b a l l m i l l i n g . How- ever, the most f requent use i s found i n con junc t ion w i t h s i n g l e stage b a l l m i l l i n g . This i s the one e f f i c i e n c y fac - t o r t h a t i s r e l a t e d t o Work Index as i s seen . i n the f o l l o w - i n g equation:

. .

F . where Rr = Ra t i o o f reduc t i on = (10)

Fo = Optimum feed s i ze R o d m i l l i n g : 16,000 (11

When ava i l ab le , use the Work ~ndex ' f r om a g r i n d a b i l i t y t e s t a t the de- s i r e d g r i n d f o r Wi i n equat ion 9. For equat ion 11, use e i t h e r the Work Index from an impact t e s t o r a rod m i l l g r i n d a b i l i t y t es t , whichever i s h igher. For equat ion 12, use the Work Index f rom a rod m i l l g r i n d a b i l i t y t e s t , s ince th is .more represents the coarse f r a c t i o n o f t he feed; i f n o t a v a i l a b l e then use the bal.1 m i l l g r i n d a b i l i t y t e s t r e s u l t s .

EF5 - Fineness o f Gr ind Factor - t h i s app l ies t o f i n e g r i nd ing when the 80% passing s i z e of the product i s f i n e r than 75 micrometers (200 mesh) .- The equat ion t o determine t h i s i s :

EF6 - High o r Low Ra t i o of Reduction Rod M i l 1 i n g - the equat ion t o be used, unless Rr i s between Rro = -2 and, Rro = +2 i s :

5 L where Rro = 8 + - D (15)


L = Rod Length

Th is f a c t o r always app l i es t o low r a t i o s o f reduct ion b u t i t s a p p l i c a t i o n t o h igh r a t i o s o f reduct ion i s n o t always needed, b u t should be used f o r m i l l s i ze s e l e c t i o n whenever Wi from the r o d m i l l and b a l l m i l l g r i n d a b i l i t y t e s t s ex- ceed 7.0.

EF, - Low Rat io o f Reduction B a l l M i l l - the need t o use t h i s f a c t o r does n o t occur very o f t e n as i t on l y app l ies t o b a l l m i l l i n g when the Ra t i o o f Reduction i s l ess than 6. Th is shows up p a r t i c u l a r l y i n reg r i nd ing concentrates and t a i l - ings. The equat ion f o r t h i s i s :

EF8 - Rod M i l l i n g - a study o f rod m i l l operat ions shows t h a t rod m i l l performance i s a f f e c t e d by the a t t e n t i o n given t o pre- pa ra t i on and feeding a un i fo rm top s i z e feed s i z e t o the m i l 1 and the care given t o main ta in ing the rod charge. Th is e f f i c i e n c y f a c t o r has no t been d e f i n i t e l y determined. I n s e l e c t i n g rod m i l l s based upon power ca l cu la ted from gr indab i 1 i t y tes t s , t he f o l l owing procedure has been recommended :

1 ) When c a l c u l a t i n g rod m i l l power f o r a rod -m i l l i ng -on l y app l i ca t i on , use an i n e f f i c i e n c y f a c t o r o f 1.4 when the feed i s t o be prepared w i t h open c i r c u i t crushing, and use 1.2 when the feed i s t o be prepared w i t h c losed c i r - c u i t crushing. The m i l l diameter, low o r h igh r a t i o o f reduct ion , and overs ize feed f a c t o r s a l so must be ap- p l i e d t o the ca l cu la ted g r i n d i n g power.

2) When c a l c u l a t i n g rod m i l l power f o r a rod m i l l - b a l l m i l l c i r c u i t , do no t a l l ow f o r improvement i n the b a l l m i l l performance due t o rece i v ing rod mi 11 feed. I f the rod m i l 1 feed i s produced w i t h open c i r c u i t crushing , apply a 1.2 i n e f f i c i e n c y f a c t o r t o the power c a l - cu la ted f o r t he rod m i l l i n g stage on ly . I f the r o d m i l l feed w i l l c o n s i s t e n t l y be the same size, such as produced w i t h c losed c i r c u i t crushing, do n o t apply a r o d m i l l i n e f f i c i e n c y f a c t o r . The m i l l diameter, low o r h igh r a t i o o f reduct ion , and overs ize feed f a c t o r s should be app l i ed t o the ca l cu la ted g r i n d i n g power.

GRINDING POWER CALCULATIONS AND GRINDING MILL SELECTIONS

The f o l l o w i n g demonstrates the use o f the Bond Work Index Method t o . determine the power requ i red t o produce the des i red gr ind . A f t e r the


g r ind ing . power has been determined by t h i s o r o ther methods, t he m i l l ( s ) t h a t w i l l draw the requ i red power can be selected. For f i n a l m i l 1 s i z e recommendations a1 1 the process design data and con t ro l 1 i n g economic and geologic fac tors should be given t o g r i nd ing m i l l manufac tu re rs and t h e i r recommendations obtained.

With the growth o f m i l l s izes and changing economic s i t u a t i o n s new fac- t o r s in f luenc ing g r i nd ing power ca l cu la t i ons and mi 11 s i ze se lec t i on a re becoming known and more w i l l become known. The g r ind ing m i l l man- u f a c t u r e r ' s are a good source f o r t he app l i ca t i on of t h i s con t i nua l l y growing technology i nc lud ing the p r a c t i c a l appl i c a t i o n o f the newer approaches and math model i n g being developed t h r u academic research.

A. . Rod M i l l s

F = 18,000 micrometers. P = 1,200 micrometers. Wi = 13.2

E f f i c j ency Factors: E F ~ does n o t apply.

EF2 does no t apply.

EF3 determine a f t e r power ca l cu la t i ons i s completed.

EF4 Feed s i z e ' i s coarser than 16,000 micrometers.

EF5 does n o t apply.

EF6 w i l l no t apply as r a t i o o f reduct ion w i l l be w i t h i n Rro +2.

Rro determined a f t e r m i l 1 s i ze se lec t ion .

EF7 does no t apply.

268 MINERAL PROCESSING PLANT.DESIGN

The rod mi 11 feed w i l l be prepared by closed EF8', . . c i r c u i t crushing a i d the rod m i l l w i l l , b e i t i *. . a r o d m i l l - b a l l m i l l ( o r pebble m i l l ) c i r c u i t ' : .

w i t h -no in termedia te concent ra t ion stage'-so -no , . EF fac to r need be-'applied.' I f ' i t were j u s t a' ..

r og m i l 1 i n g c i r c u i t ' o r i f the re were -an i n t e r - mediate concent ra t ion stage between the r o d and. the m i l l . , a 1.2 f a c t o r would apply.

. , . .

, , . c * .

conversion sho r t t0.n t o m e t r i c t o n n e 1.102 . . . . K i l owa t t s . t o horsepower 1.341 .

. .

2.83 x 1.06 x 1 . I02 x 1.341 = 4.43 ~ph/metr i 'c ' tonn.e 4.13. x 500 = 221 5 HP - * . - .

Re fe r r i ng t o Table V two m i l 1 s w i 11 be required. The 'pre- l i m i n a r y r o d m i l l se lec t i on would be a 3.66 meter (12 f o o t ) i n s i d e s h e l l 3.46 meter (1.1.35 f o o t ) diameter i n s i d e new s h e l l 1 iners . Re fe r r i ng t o Table I X the EF3 (Diameter E f f i - c iency) f a c t o r i s 0.931.

Re fe r r i ng t o Table V the 3.66 m x 4.88.111 rod m i l l w i t h 4.72 m (15.5 f t . ) l ong rods ca l cu la tes t o draw 972"HP. when ca r r y - i n g a 40 percent rod charge. w i t h a worn-in bu lk dens i t y o f 5606 kg per cub ic meter (350 pounds per cub ic f o o t ) . 1031 HP i s required. Therefore, increase m i l l l eng th by 0.3 meters (1 f o o t ) .

Therefore, use two 3.66 meter .(.I2 f o o t ) diameter i n s i d e s h e l l 3.46 meter (11.35 f o o t ) diameter i n s i d e new,she l l li- mers by 5.18 meter (17.0 f o o t ) l ong over f low rod m i l l s w i t h a 40 percent by m i l l . volume rod charge,wi t h 5.02 meter (16.5 foo t ) long rods.

The'refore, E F ~ assumption i s confirmed. . .

These m i l 1 s a re requ i red t o prepare b a l l mi 11 feed.

With pebble m i l l i n g the pebble p o r t i o n o f the product does n o t go t h r u the rod m i l l thus the r o d m i l l feed r a t e i s r e - duced by 30 'met r ic tonnes per hour (6% o f 500 m e t r i c tonnes pe r hour) .

ROD AND BALL MILLS: . '

Therefore, use two 3.66 meter (12 f o o t ) diameter i n s i d e s h e l l 3.46 meter (11.35 f o o t ) i n s i d e new s h e l l l i n e r by 4.88 meter (16 f o o t ) l ong over f low rod m i l l s w i t h a 40 percent by m i l l volume rod charge w i t h 4.72 meter (15.5 f o o t ) l o n q r o d s .

. . . . Rr.,= 15.0 . .

~ t i k r e f ~ r ~ , ' E F ~ a s i i m p t i ' a n i s a1 so . c 6 f i r . h e d .


f o o t ) over f low b a l l m i l l w i t h a 40 percent by m i l l volume b a l l charge, new she1 1 l i n e r s and 64. mm (2.5") diameter b a l l s draws 1266 HP.

3.96 x.1.46 =.5:78 meters (18.96 f e e t ) Therefore, use two 4.12 meter (.13.5 f o o t ) diameter i n s i d e s h e l l 3.93 meter (12.9 f o o t ) diameter i n s i d e new l i n e r s by 5.79 meter (19.0 f o o t ) l ong over f low b a l l m i l l s w i t h a 40 percent by volume b a l l charge.

For lower opera t ing costs, s l i g h t l y b e t t e r e f f i c i e n c y , and b e t t e r m i l 1 a v a i l ab i 1 i t y the cu r ren t p r a c t i c e favors over- f l o w b a l l m i l l s however, t he re are some operators t h a t pre- f e r g ra te d ischarge m i l l s . Re fe r r i ng t o Table V I I a 3.96 meter (13.0 f o o t ) diameter by 3.96 meter (13.0 f o o t ) d ia - phragm b a l l m i l l w i t h a 40 percent by m i l l volume b a l l charge, new s h e l l 1 i n e r s and 50 mm (2" ) diameter b a l l s draws 1311 HP.

3.96 x 1.41 = 5.58 meters (18.3. f e e t ) , .,

Therefore, use two 3.96 meter (13.0 f o o t ) diameter i n s i d e s h e l l 3.78 meter (12.4 f o o t ) diameter i n s i d e new l i n e r s by 5.79 meter (19.0 f o o t ) long diaphragm (g ra te ) d ischarge b a l l m i l l s w i t h a 40 percent by volume b a l l charge.

C. B a l l M i l l s : S ing le Stage-

The feed t o the standard Bond b a l l m i l l g r i n d a b i l i t y t e s t i s minus 6 mesh. Thus, the coarser f r a c t i o n o f a minus 112" s ing le-s tage b a l l m i l l feed i s n o t inc luded i n the feed t o t he g r i n d a b i l i t y b a l l m i l l . The minus 112" feed t o a stand- a r d Bond r o d m i 11 g r i ndabi 1 i t y t e s t , however, does i nc lude t h e coarse f r a c t i o n o f a s ingle-stage b a l l m i l l feed. To o b t a i n t he complete g r i n d a b i l i t y p r o f i l e (Wi vs s i z e ) o f an o r e when s e l e c t i n g a s ing le-s tage b a l l m i l l , i t i s adv is - ab le t o run both rod and b a l l mi 11 gr indab i 1 i t y t e s t s . If there i s a d i f f e r e n c e i n the work i n d i c e s obtained f rom the r o d m i l l and the b a l l m i l l g r i n d a b i l i t y t es t s , which f requent ly occurs, then, p a r t i c u l a r l y i f the rod m i l l t e s t work index i s h igher, a two-step c a l c u l a t i o n should be made t o determine the requ i red g r i nd ing power. . The rod m i l 1 work


index should be used t o c a l c u l a t e from the p l a n t b a l l m i l l feed s i z e t o 80% passing 2100 microns. The c a l c u l a t i o n from 2100 microns t o the des i red product s i z e i s made us ing the work index from the bal ' l m i l l g r i n d a b i l i t y t e s t . The sum o f these two gives the t o t a l uncorrected power per t on re - qu i red f o r g r ind ing. ,

F .= 9,400 micrometers. . . P = 175 micrometers. Wi = Rod m i l l t e s t 13.2. Wi = B a l l m i l l t e s t 11.7.

Step one: w = - 132 - 132 = 1.52'kwhIs. ton

Q;roO Jm . , Step two: .

w = - 177 - 117 = 6.'29 kwhls. ton m $ 2

-

. T o t a l , .. .

7.81 kwhls. ton . .

7:81 x 1.102 x 1.341 x 500 = 5766 HP, uncorrected.

E f f i c i e n c y Factors:


EF2 ' does n o t apply.

EF3 M i l l s w i l l b e . l a r g e r than 3.81 meter i n . diameter so use 0.914.

EF4 Feed i s coarser than 4000 micrometers.

Rr = 9,400 i 175 = 53.7

Fo = 4,000 -2 = 3970

. ,

- EF5, EF i , EF7 and E F ~ do n o t apply.

5766 x 1.12 x 0.914 = 5903 HP


Use 2 m i l l s

Per Table V I t he LID should be around 1.25. Re fe r r i ng t o Table V I I a 5.03 meter (16.5 f o o t ) diameter by 4.88 meter (16.0 f o o t ) over f low b a l l m i l l w i t h a 40 percent by m i l l volume b a l l charge, new s h e l l l i n e r s and 64 mm (2.5") d ia - meter b a l l s draws 2370 HP.

' . ' .

4.88 x"1.25 = 8.1 meters ' (20.0 f e e t ) Therefore, use two 5.03 meter (16.5 foo t ) diameter i n s i d e s h e l l 4.85 meter (15.9 f o o t ) diameter i n s i d e new l i n e r s by 6.1 meter (20.0 f o o t ) l ong over f low b a l l m i l l s w i t h a 40 percent by volume b a l l charge.. . .

Re fe r r i ng t o Table V I I . f o r s i z i n g a g ra te discharge m i l l a 4.72 meter (15.5 f o o t ) di'ameter by 4.57 meter (15.0 f o o t ) g ra te d ischarge b a l l m i l l w i t h a 40 percent by m i l l volume b a l l charge, new she1 1 1 i n e r s and 64 'inn '(2.5") diameter b a l l s draws 2269 HP. . . .

. : . . . -

4.57 x 1.3 = 5.94 meters (19.5 f e e t ) Therefore, use two 4.'72'.meter (15.5 foot,) diameter i n s i d e s h e l l 4.54 meter (14.9 f o o t ) , d iameter ' i n s i d e new 1 i n e r s by 6.1. meter (20.0 f o o t ) l ong diaphragm (g ra te ) d ischarge b a l l m i l l w i t h a 40 percen i by volume b a l l charge.

D. B a l l M i 11 : ~ o l lowing ~ u t b ~ e n o " s br s e m i - ~ u t o ~ e n o u s pr imary M i l l . . . . ,

. / . ..

If the product s i z e from the pr imary autogenous o r semi-autogenous m i l l i s the same' as from a rod m i l 1, the b a l l m i l 1 c a l c u l a t i o n and s i z e s e l e c t i o n i s the same as covered under sec t i on B above. I f the b a l l m i l l feed s i z e i s d i f f e r e n t f rom t h i s , t he same procedure as covered by e i t h e r sec t i on B o r C (whichever app l i es ) should be used t o determine g r i nd - i n g power, and b a l l m i l l s i z e .select ion.

' ROD AND BALL MILLS

E. - Pebble M i l l : Rod ~ i l l ' p e b b l e M i l l C i r c u i t

The c a l c u l a t i o n for . .determining g r i nd ing power f o r Pebble m i l 1 i n g (secondary autogenous) can be the same as f o r b a l l m i l l i n g f rom r o d m i l l product s i z e t o the des i red spec i f i ed s ize, neg lec t i ng the diameter e f f i c i e n c y f a c t o r i f less than

I . 1.0.

5.47 x 1.102 x 1.341 x 500 = 4039 HP

To t h i s add the power requ i red t o wear the pebbles down t o .rod .mi l 1 product s i z e (pebble m i l l feed ' s i ze ) .

F = 70,000 micrometers. P = 1,200 micrometers. Wi = 13.2

The i n e f f i c i e n c y f a c t o r t o a l l ow f o r the i n e f f i c i e n t use o f power i n wearing down from pebble s i z e t o rod m i l l product

I s i z e i s 2.0.

Se lec t two 2200 HP pebble m i l l s . For s p e c i f i c s i z i n g r e f e r t o m i l l 'manufacturers f o r recommendations as they have pro- p r i e t a r y equations fo r c a l c u l a t i n g mi 11 power draw tak ing i n t o account the var ious ore media and pu lp f a c t o r s involved.

F. Regrind B a l l M i l l

F = 210 micrometers. ' ' P = 45 micrometers. Wi = 14.0

E f f i c i e n c y Factors:



EF Many r e g r i n d operat ions a re c losed c i r c u i t , bu t assume t h i s one i s open c i r c u i t and 80. percent passing g r i n d w i l l be the c o n t r o l l i n g p o i n t . Re- f e r t o Table V I I I . The EF2 f a c t o r i s 1.2.

EF3 Because b a l l s w i l l be smal ler than 40 mm (1.5") . and o the r minor f a c t o r s neg lec t EF unless m i l l

diameter i s l e s s than 2.44 meter (3.0 ' ) diameter i n s i d e l i n e r s .


E F ~ Gr ind i s 80 percent passing 45 micrometers.


EF7 Rr = 210 + 45 .= 4.67 which i s l ess than 6;


Re fe r r i ng t o Table V I the L I D can be between 1.75 and 2.0 o r even greater . Re fe r r i ng t o Table V I I a 3.05 meter (10 f o o t ) by 3.05 meter (10 f o o t ) over f low b a l l m i l l w i t h a 40 percent by mi 11 volume b a l l charge, new 1 i n e r s and 50 mm (2 " ) b a l l s draws 491 HP. Using equat ion 5 there w i l l be a l oss o f 0.55 Kw (0.74 Hp) per me t r i c tonnes o f b a l l s .

3.05 x 1.91 = 5.83 meters (19.1 f e e t ) Therefore, use one 3.05 meter (10.0 f o o t ) diameter i n s i d e s h e l l 2.89 meter (9.5 f o o t ) diameter i n s i d e new l i n e r s by 5.79 meter (19.0 foo t ) l ong overf low b a l l m i l l w i t h a 40 percent by volume b a l l charge. For rubber l i n e r s add 10% o r 0.58 meters (approximately 2 ' f ee t ) t o the length .

G. Motor Se lec t i on

I n a l l cases the m i l l s should be d r i ven by a l a rge enough motor t o a l l ow the m i l l t o operate w i t h a 45 percent by mi 11 volume charge w i t h new l i n e r s and a t l e a s t a 36 percent charge w i t h worn l i n e r s . It may be des i red t o u t i l i z e more o f the a v a i l a b l e m i l l volume as the l i n e r s wear so a h igher charge can be spec i f i ed f o r worn l i n e r s . Spec i f i ca t i ons can a l so c a l l f o r the d r i v e and motor t o be ra ted t o a l l ow using p in ions w i t h one l ess and two more teeth, thus a l l ow ing f o r changing mi 11 speed if it i s found necessary t o balance c i r - c u i t , increase capaci ty, s u i t changing ore cha rac te r i s t i cs , e t c .

SELECTION OF GRINDING MEDIA SIZES AND ESTIMATING STEEL CONSUMPTION

The equat ion f o r se lec t i on o f the l a r g e s t diameter rod f o r the i n i t i a l charge and f o r t he make-up charge i s :

R = Diameter o f rod i n m i l l ime te rs . F = Feed s i ze 80% passes i n microns. W . = Work Index. S' = S p e c i f i c Grav i ty . C: = C r i t i c a l Speed. D = Diameter i n s i d e she l l l i n e r s i n meters.

With R i n inches and diameter (D) i n f e e t equation 17 becomes:

Table X g ives t h e e q u i l i b r i u m s ta r t -up rod charge f o r t op rod s izes from 125 mm ( 5 " ) t o 65 mn (2.5") . The equation fo r s e l e c t i o n of the l a r g e s t diameter b a l l f o r the i n i - t i a l charge and f o r t he make-up charge i s :

B = (18)

- J B = Diameter o f b a l l i n m i l l ime te rs .

NOTE: Except f o r K which i s g iven below a l l o ther terms the same as f o r equation 17.

276 MINERAL. PROCESS.ING PLANT DESIGN

TABLE X .

START-UP EQUILIBRJA GRINDING ROO CHARGES, PERCENT WEIGHT . ,

Make-Up Rods ~ e d Sizes , MM= R 125 . 115 100 90 75 65

T,OTAL Pct 100 100 100 100 100 ' 100 . .

TABLE X I

Make-Up B a l l s Fed

Sizes, MM= B

115 (4.5") 100 (4.0") 90 (3.5") 75 (3.0") 65 (2.5") 50 (2.0") 40 (1.5") 25 (1.0")

TOTAL PC. 100.0, 100.0 100.0 100 100. 100 100

" ROD AND BALL MILLS

.Ba l l . Mi11 K Factor '

M i l l Type and . .

Steel o r Gr ind ing C i r c u i t . C.1: B a l l s

K

' Wet-Overf 1 ow-Open C i r c u i t Wet-Overfl ow-Closed C i r c u i t Wet-Diaphragm-Open C i r c u i t .

. .

Wet-Diaphragm-Closed.Circui t Dry-Diaphragm-Open C i r c u i t Dry-Diaphragm-Cl osed C i r c u i t

Wi th B i n inches and diameter .(D) . i n f e e t equat ion 18 becomes:

Table X I g ives . the e q u i l i b r i u m s ta r t -up b a l l charge f o r t o p + b a l l s izes f rom 115 mm (4.5"). t o 40 mm (1.5"). These two equations g i ve the l a r g e s t diameter o f the g r i nd ing media requi'red. Since the ca l cu la ted s i z e i s n o t always an a v a i l a b l e stand- a r d s i z e s e l e c t t he nearest l a r g e r s i z e ava i l ab le . Actual opera t ing experience may d i c t a t e a change from the ca l cu la ted s ize . Theoret ic- a l l y i t i s always adv isab le t o use a graded charge as a replacement charge. Using a graded charge o f ten i s no t p r a c t i c a l . The l oss i n e f f i c i e n c y by n o t us ing a graded charge genera l ly can n o t be measured. I n some cases, i t i s on l y necessary t o add the l a r g e s t s i z e media c a l - c u l a t e d as make-up. Operating r e s u l t s w i l l i n d i c a t e the necess i ty o f us ing more than one s i z e of media i n the make-up charge.

The bes t f i g u r e s f o r media and l i n e r consumption come from ac tua l oper- a t i n g experience and as opera t ing data i s generated t h i s should be used t o e s t a b l i s h wear ra tes .

Actual t e s t i n g i n l abo ra to ry scale equipment t o determine the abrasion c h a r a c t e r i s t i c s o f an ore i s d i f f i c u l t , and a v a i l a b l e t e s t s are guides f o r es t imat ing purposes b u t a re n o t completely accurate. One abrasion t e s t measures the weight l oss o f a s tee l paddle cont inuous ly impact ing f a l l i n g ore p a r t i c l e s f o r a prescr ibed t ime per iod under standard con- d . i t ions . From t h i s i s developed a measurement c a l l e d an abrasion In - dex, A i . From p l a n t data, emperical equations c o r r e l a t i n g w i t h A i : were developed t o be used t o est imate rod, b a l l , m i l l 1 i n e r and crusher 1 i n e r wear ra tes . . These equations are:

Wet Rod M i l l s : Rods, kg/Kwh = 0.175 ( A i - 0.020)'2


L iners , kglKwh = 0.175 ( A i - 0 . 0 1 5 ) ' ~ (20 Wet B a l l M i l l s :

Ba l l s , kg/Kwh = 0.175 (A i - 0.015) 113 (21 ) L iners , kg/Kwh = 0.013 ( A i - 0 . 0 1 5 ) ' ~ (22

M u l t i p l y equations 19, 20, 21 and 22 by 2.2 t o get pounds per k i l o w a t t .

These formulas g i ve est imates o f wear r a t e s which can be used as a guide. They a re sub jec t t o such th ings as m i l l speeds, percent vo lu- m e t r i c loading, a l l o y o f g r i nd ing media and l i n e r s , opera t ing prac- t i c e s , e t c .

The re ference in format ion used t o prepare t h i s was:

Bond F. C.

Rowland C. A. "Gr inding Ca lcu la t ions Re,lated t o the Appl i- c a t i o n o f Large Rod and B a l l M i l l s " , A l l i s - Chalmers Pub l i ca t i on 22P4704.

Bond F. C. "Gr inding B a l l Size.Select ion", Mining Engi- nee r i ng . May, 1958. . .

Rowland C. A. "App l i ca t i on o f Dry Gr inding Rod M i l l s " , & Nealey R. C. Transact ions o f Society o f Mining Engineers

o f A.I.M.E.

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Ch 12 Rod & Ball Mills