Scale-up and Dynamics of Large Grinding Mills - A Case Study

7/25/2019 Scale-up and Dynamics of Large Grinding Mills - A Case Study

1/19

Design and Installation

of

omminution ircuits

Co Editors

Andrew L

Mular

Professor of

Mineral

Process Engineering

University of British Columbia

Vancouver B. C

Canada

Gerald V. Jergensen II

Tucson

Arizona USA

This

volume

was originated by the Mineral Processing Division

of

the Society

of Mining

Engineers of AIME to serve as a practical

textbook o

current comminution design

and installation practice.

Richard Addison

Derek J Barratt

James

E

Coburn

Dale Dixon

Robert EIsner

Malcolm D. Flavel

George

A.

Grandy

Editorial Board

Society of Mining Engineers

of the

Richard W.

Harper

Leonard Harris

S.G. Malghan

R E

. Mcivor

Stanley

M. Moos

Fred Pena

Mathew

A.

Sochocky

American Institute of Mining Metallurgical and Petroleum Engineers Inc.

New

York

New

York1982


2/19

Chapter 6

SCALE-UP

ND

DYN MICS OF L RGE GRINDING MILLS - A CASE STUDY

Nathaniel Arbi t e r

and

Colin

C.

Harr is

Henry Krumb

School

of Mines

Columbia

Univers i ty

New York, N.Y . 10027

~ s t r c t

Curren t

sca le -

up

procedures

are

s c u s s e d c r i t i c a l l y

inc luding:

= . s t an t sp ec i f i c

energy c r i t e r ion ;

~ t e r m i n a t i o n of mi l l

s i ze and

power

a

given

ore , th roughput

and mesh

gr ind;

sp ec i f i ca t io n

of opera t ing

S?eed and load ing . A major dynamic

k in e t i c fac to r now

recognized i s

~

the

r a t i o of

media

ro ta t iona l

=-ow to ore

ax ia l f low,

and

the

num

=e

r

of mil l r evo lu t ions

t ha t

ore i s

s j ec ted to dur i

ng

r es idence , both

i n i s h as m

ill

diameter i nc reases .

= e s e fac to rs can

lead

to

capac i ty

i t a t i o n s when

mil l

diameters reach

a c r i t i c a l

range

e spe c i a l l y

r egard

~

coar se

s izes .

Exper ience a t the

g a in v i l l e

and Pin to Valley opera

=i

ons

i s cont ras t ed .

Correct ive

-

asures

s u

ggested

are

to

reduce

o a d i n g

and

inc rease speed towards

~ e Davis b es t

opera t ing

speed.

-

t r oduc t ion

Although

problems

in sca le -up

f gr ind ing mil l s are r a re ly

r epor ted

~ e c e n t

publ i ca t ions by

the

s t a f f

o f

30uga inv i l l e Copper

Ltd.

Hinkfuss

~ 9 7 6 ;

Steane

and Hinkfuss , 1979;

~ l y a r d

1981) have

revealed

a se

r

ous discrepancy between the

des ign

49

c r i t e r i a

for the capac i ty

o f

t h e i r

5.9m 18 f t )

b a l l

mil l s

and a c t ua l

cap ac i t i e s

in product ion. These

publ i ca t ions

provide in format ion

a t

the

same

t ime

which

suggests

previous ly unrecognized e f f ec t s o f

increased diameter

on

gr inding

mil l

dynamics.

The

discrepancy

a t

Bougainvi l le

has

l ed

to

recommenda

t ions t h a t mi l l s of

s imi la r

s i ze

should not be

i ns t a l l ed

e l sewhere

u n t i l the Bougainvi l le

problem i s

b e t t e r

understood

Kjos, 1979).

This i s

in

s p i t e of the fac t

t h a t

mil l s of

i d en t i ca l

s i ze opera t ing

a t

the

Ci t i e s Serv ice Pin to

Val ley

Concent ra tor , are performing

s a t i s f a c t o r i l y Kennedy, 1982) .

This

chapte r analyzes the

problem

in d e t a i l and suggests poss ib le

so lu t ions fo r

it Fur ther

di scus

s ion and

bas ic

in format ion has been

provided

elsewhere Arbi ter

and

Harr i s ,

1980;

Harr is

and

Arbi t e r ,

1982) .

SC LE - UP PROCEDURES

Scale - up procedures cur ren t ly

involve

the

fo l lowing

s teps in

o u t l i n e :

1 . Est imat ing the sp ec i f i c

energy

requirement


3/19

49

DESIGN INSTALLATION OF OMMINUTION CIRCUITS

[power / t ons /h r )] fo r t he

p a r t i c u l a r

ore a t a spec

i f i e d feed

s i ze and

mesh

of g r ind .

2 . From

t h i s

and des ign

tonnage

ra t e ,

es t imat ing t he

t o t a l

power requirement .

3. From t o t a l power and

manu

f ac tu re r s

' t ab l es ,

char t s ,

or equa t ions , es t imat ing

t he

s i ze

and number of

mi l l s .

Spec i f i c Energy Requirement

In

t he

twent ies (Taggart , 1927) ,

lump sum

averages

were given

for

the

energy

to

grind

to

a p a r t i c u l a r mesh ,

with minor

a t t en t ion

to

feed s i ze .

Ore qr indab i l i t y dif fe rences

were

recognized by

recommending a

50 per -

cen t increase fo r hard ores ,

and

r educt ion

fo r

so f t e r

ores somewhat .

It i s o f i n t e r e s t

t ha t

t he energy

f igures

do not

d i f f e r

s ign i f i can t ly

from

those

ca lcu la t ed

using the

average

Bond Work

Index

for copper

ores app l ied to a 0 . 5

in

feed s i ze

and to

t he

ind ica ted produc t s i zes .

By t he t h i r t i e s

and for t i e s

s t andard gr indab i l i ty

t e s t s

were

widely

used,

d i f f e r i n g in de t a i l

with

d i f f e ren t manufacturers . The

r e su l t s

were

appl ied

, along wi th those fo r

comp ar i son ores for which commercial

operat ing da ta

were

on

f i l e ,

to

e s-

t imate spec i f i c

energy . Within t he

l a s t

two

decades,

the Bond Work Index

has become an indus t ry s tandard .

The

Index

i s

ac tua l ly

an

energy/ ton

pro-

p o r t i o n a l i t

y cons tan t ; it re fe rences

t he gr i nda b i l i ty fo r a p a r t i c u l a r ore

and

mesh,

which i s a

gr ind ing

r a t e

[MT-1],

t o a s t andard gr inding r e f -

erence opera t ion . The r esu l t i ng

Index

i s

then

used

by proport ioning

t o

ob ta in

t he energy /

ton

fo r

the

design

spec i f i ca t i on

,

and th

en t he

t o t a l

power requirements . Correc t ion

f ac to r s

a re

a p p l i ed

fo r

such

i tems

as : dry versus wet

gr inding;

open

versus closed c i r c u i t ; excess ive

coa r seness

o f feed o r

f ineness of

gr ind ,

and

m il l diameter . One m ~ -

diameter f ac to r used, [ 8 /0 )0 . 2 ] ,

reduces

the r e l a t i v e

power

requ i r e -

ment

as

m il l diameter

increases

to D l 2 . 5 f t

(3 .8

m);

t he rea f t e

r

it

remains

unchanged a t

0.914

(Rowland and Kjos,

1978)

.

As

befo re ,

manufacturers '

, da::.:.

fo r

power

and m i l l

s i zes

are

use

d

to

determine t he

s i ze and nu

mber

mi l l s .

Other

des ign

c r i t e r i a

and

des igner p refe rences

based

on ex

pe

r i ence a re

used

fo r

t he d e t a i l s

o=

t he gr ind ing c i r c u i t ; in

par t i cu

la=

these may a f f e c t t he

type

o f mil

l

and the s i ze and number o f mi l l s ,

in r e l a t ion to fol lowing c i r c u i t s

and

to ove ra l l design

cons t ra in t s

.

The

s i ze arid

number

o f m il l s

w i l l depend

to some extent

on whi

manufacturer

' s d a t a

are

used . Fo r

example, m il l

s i zes

pred ic ted b y

d i f f e r e n t

manufacturers

for a 1 00

HP

power requirement

are as fo l l o ;;o :

l

10

X

19

f t . Lf

= 40 ,

fc=

2.

ll X 15 f t . Lf = 40 ,

fc

=

3.

11.9 X 1 2 f t .

Lf=

45 , fC= 71. 8

4.

1 0 X 16 f t .

Lf

= 45%, fc =

75

The d i f f e r ences

are due

to

causes:

( l)

d i f f e r e n t

manufact

urerE

recommend d i f f e r e n t load f r ac t io ns

and

m il l

speeds;

and

2) ,

even

f o r

the same operat ing condi t ions d i f -

f e ren t m il l s i zes

may

still

be

spec i f i ed .

Discuss ion

Three impor tant aspec t s o f t he

manufacturers es t imat ing

procedures

need

c l a r i f i c a t i on .

l .

The

form

and

r e l i a b i l i t

y

of the r e l a t i onsh ip use

to es t imate

power as

a

funct ion o f m i l l s i z e a = ~

opera t ing cond i t ions ,

such

as speed

and lo a

d.


4/19

DYN MICS OF

L RGE

GRINDING

MILLS

49

2. The

unexplained

imposi t ion

o f

a

decreas ing

f rac t ion

c r i t i c a l

speed

( fcs)

re

quirement wi th i ncreas ing

m i l l

diameter

recommended

by

severa l

manufac turers

( fcs D-O.l

to D-O.l5)

3.

The un iver sa l

assumption

t h a t constancy of app l ied

energy/ ton

i s the

i nvar

i ab le

and only

c r i t e r i o n

fo r scale-up. Each o f

these

fac to rs wi l l

be

b r i e f l y discussed,

s ince

each has

a

bear ing on the

Bougainvi l le

problems.

Power

Pred ic t ion

Power consumption,

im p l i c i t l y

independent o f gr ind ing ac t ion , i s

almost always

es t imated

by app l i ca

t i o n

of some

form of

the torque

-

arm

equat ion (Hancock, 1934) ,

wi th l

ittl

demons t ra t ion in the p as t

t ha t opera

t i n g

mi l l s conform. However, Kjos

(1979)

has shown

t h a t the

A l l i s

Chalmers modi f ica t ion o f the

equat ion

does pred ic t power

d r a f t

with

ac

curac ies with in

a

few

percen t for

l a rg e r

ba l l

and

rod

mil ls .

A

s impler equat ion,

P/WND(l

- Lf) constant

(Harris and Arbi t e r , 1982) , (see

appendix

fo r der iva t ion) can be

app l ied to

much ava i lab le

opera t ing

data (Taggart , 1945;

Kjos,

1979) and

holds

su f f i c i en t ly

wel l for pre l im

ina ry es t imat ing . The constant has

the

fo l lowing

values

according to

mil l type:

Type of

Mil l

WND(l-Lf)

a o

f

c

Grate

0.13

54 0.78

Tube

0.12

48

0.76

Autogenous

O. l l5

45

Overflow

O. l l

43

0.68

Rod 0.09

34

0.59

The i nd ica t ed

angle ,

a , i s t h eo re t

i ca l l y the angle o f i nc l ina t ion of

the charge surface

to

the hor izon ta l

(angle o f repose) , but

in view

of

var ious

imprecis ions in

us ing

the

equat ion

fo r operat ing

m il l s ,

the

absolute angle values a re not con

s idered s i g n i f i c a n t

.

However, the

apparent value

i s

ind ica t ive

of

d i f fe rences

in

both

f r i c t i o n a l

coe f f i c i en t s within the load

and

o f

load ag a i n s t

the l i ne r s ; a l so the

angle depends on t he average

f r ac

t i ona l

c r i t i c a l speeds

. Tagg ar t s

1945 opera t ing

data

show t h a t the

average power coe f f i c i en t s

and

angles

ca lcu la ted from

them

decrease reg

u la r ly with average fcs

values

.

The

mean value and d i sper s ion

for

the

power

coe f f i c i en t s

are

0. ll . 01. Compared

to

impe l le r

t ank power

coe f f i c i en t s

in mixing

and

f lo t a t ion c e l l s , which show about

a t en - fo ld range ,

the va r i a t ion

in

coe f f i c i en t s fo r g r ind ing mil l s i s

r e l a t i ve ly small :

10 percen t .

This

argues

t ha t

v a r i a t i o n s

in the

media /mi l l

l i n e r

shape

f ac to r s have

fa r

l e s s

in f luence on mil l

power

d r a f t

than

do t he im pe l l e r / s t a to r

b a f f l e conf igura t ions in s t i r r e d

tanks .

Another fac to r

in power

es t ima

t i on , which i s usual ly neglected , i s

the weight

o f

pulp hold-up.

The

charge

densi ty i s cus tomari ly

taken

as

290-300 lb s /cu

f t for

b a l l s

and

340-390

lb s /cu

f t

fo r

rods , both

f igures

based on the apparent

dens i ty

o f

a

s ta t ionary

load

(appendix

Table

A2). Actual ly , the

ro ta t ion

o f the mil l

causes

expansion of the

voidage o f

the

load in propor t ion to

the speed as shown in appendix Tables

A and

7 .

This can r e su l t

fo r a 45

percen t

load

f r ac t i o n

in

voidages

from

29

to 39 p er cen t , i n s t ead

o f

19

percen t fo r b a l l m i l l s ;

and

in

voidages

of

from

22 to 26

percen t fo r

rod m il l s . These a re

for

speeds

from

60

to 80 percen t o f c r i t i c a l .

Taking

in to account the

e f f e c t

of presence

o f pulp as void f i l l i ng on power ,

draw

r esu l t s

in

a

10

to

15 percen t


5/19

9

DESIGN INSTALLATION

OF OMMINUTION

CIRCUITS

i ncrease i n ca l cu l a t ed

values

fo r

b a l l mil l s and a 5 to 10 percen t in

c rease fo r rod mil l s see appendix

for d e t a i l s ) .

Recommended Mil l

Speeds

Mills

speeds used in prac t i c e

show cons ide rab le

v a r i a t i o n and

incons i s tenc ies .

In

the twent ies

8 f t 2.4 m m il l s , t he

l a rges t

then

in

use, were opera ted a t speeds

as

high as 0 .89 fcs and t here was ad

vocacy o f speeds

in t he 0.80

range

for

increased

crushing

of the coarser

p a r t

of the

m i l l

feed. However, a t

the same t ime Taggart 1927) c i t e d

data

to

show t ha t

reducing

fcs

from

0.89

to

0.57 reduced

power

subs tan

t i a l l y ,

had

no e f f e c t

on capac i ty ,

while

s ign i f i c an t ly

reducing

b a l l

and

l i n e r wear. Other data o f

the

same

per iod showed the i n t e rac t i o n s among

speed and b a l l s i ze with feed s ize

and

ore c h a r a c t e r i s t i c s ,

but

con

t ro l l ed t e s t i n g was inf requent .

There has been

a

c lea r

t rend

s ince

then toward a

reduct ion

in mil l

speeds ove ra l l , with a secondary

t rend to

reducing

fcs

with

in

c

reas ing

mil l

diameters . For

-

example,

t he

All i s -Chalmers c

ata logues

have a

b u t l t - i n reduc t ion according to

fc -

n-

0

15

fo r mil l s

l a rg e r than 9 f t

2.7

m),

with a

smal ler

propor t iona l

decrease for

smal ler

mil l s .

This i s

i l l u s t r a t e d by

fcs va lues of 0.80 a t

3ft 0.9 m);

0.78 a t

6ft 1.8 m);

0.75 a t 2ft 3.7 m); 0.70 a t

5ft

4.6 m

and

0.68 a t

8ft

5.5 m).

Similar but not

i den t i ca l

t rends are

recommended

by

o ther

manufacturers .

Constant Energy/Ton Scale-Up Cri te r ion

The power co r re l a t i o n

equat ion

previous ly

given

appendix) lends

it-

s e l f to a

simple

i l l u s t r a t i o n of the

consequences o f var ious co n s t r a in t s

on sca l e -up . It can be

t ransformed

as

fo l lows:

3

P

ND

Lp

Lf l -Lf)

where the p ro p o r t i o n a l i t y

term

i s an

appropr ia te cons tan t fo r mil l type .

With Qf the hour ly

tonnage

r a t e ,

P/Qf NDpL f l - L f ) t

where

the average

re s idence

t ime

t

i s volume/feed r a t e . At cons tan t

load

and load dens i ty

t h i s

reduces t o

energy/ ton

NDt-constant

fo r

the

convent ional sca l e -up c r i t e r i o n .

The

quan t i ty Nt has

been def ined

as

a mixing coe f f i c i en t , i

Harr is

and

Arbi te r , 1982). This v a r i e s i nver se

ly with mil l diameter

r eg a r d l e s s

of

the N vs D r e l a t ionsh ip .

Fur ther ,

i f

Nn

5

i s constant cons tant f cs ) , then

E n-

0

5

. Iff aon-

0

15

see

mil l

c

-0

65

speeds

above) then

ND and

-0

35

then

the e f f e c t o f t he reduc-

t i o n in

fc s with

i ncreas ing

m i l l

diameter

i s to modify the

reduct ion

in

res idence

t ime bu t a t the same

t ime

to

reduce

the

growth

of s p ec i f i c

capac i ty o f a mil l s ince

2.5

Qf

PD L a t cons tan t

Qf/D2L

D0.5

o r

f o r

c

2.35 -0 .15

Q

PD L a t f D o r

f c

Q /D2LD0.35

f

This

discuss ion impl ie s t h a t

sEeci f i c

capac i ty

increases

as

D

5

a t cons tan t ene rgy / ton and

cons tan t f c s , but as n0.35 a t

c

ons tan t

energy per ton

and

fcs

decreas ing as n-

0

.1

5

. Fin a l l y ,

as

shown

elsewhere

Harr is

and

Arbi te r , 1982)

the

r a t i o

o f

the

i n t e rna l flow of media

to feed

r a t e

QI/Qf, which with b a l l s i ze can be

r e l a t ed

to

the frequency o f impact

of ba l l s

with

a u n i t o f ore , a l so

v a r i e s i nver se ly

with mil l diameter .

This

r a t i o

i s a major f ac to r i n

gr ind ing k ine t i c s .

The above discussion o u t l i n e s

th ree

dynamic

fac to rs

involved

in

the

discrepancy

between

l a rge mi l l

and smal l m i l l / l ab o ra to ry

work

i nd ices :


6/19

DYN MICS OF L RGE GRIN ING MILLS

95

1 .

Reduced r a t i o o f i n t e rn a l

media

ro t a ry

flow

to

feed

flow, probably the main

k ine t ic

f ac to r .

2.

Reduced

mixing

co e f f i c i en t s

depending

on the combina

t i on Nt,

and

not on

speed

a l

one.

3 . Reduced re s i dence t imes fo r

l a r g e r

m i l l s , the ex ten t

depending upon the imposed

N vs D

r e l a t i o n .

Al l

th ree o f

these depend

in

mag

ni tude on the cons tant energy/ ton

sca l e

-

up cons t ra in t .

THE BOUGAINVILLE

SCALE- UP PROBLEM

This problem has been summarized

in d e t a i l by the

BCL

s t a f f

H

i nkfuss ,

1976; Steane and Hinkfuss , 1979;

Ti

l yard, 1981) . In b r i e f , extens ive

l abora to ry

gr indab i l i ty t e s t s on

d r i l l cores gave a

work index

o f

12.0 .

Pi l

o t

p l an t opera t ion

in

a 1 .8 x 1 .5 m

5 . 9 x 4.9 f t ) mi l l gave work

ind ices

in good agreement on

a l

l samples with

labora tory indices

on

the

same

feed .

Combined da ta gave a work

index

es t ima te

fo r the

f i r s t

f ive year s of

opera t ion

o f

11.42 . Plan t opera t ion

fo r the f i r s t s i x months however

gave

ind ices

ranging from

1 2.1 - 24.2

averaging 18.2 ,

whereas

the o r ig in a l

design

indices

were 10.5 - 13 .6 ,

averaging

12

.1 .

The

labora tory

work

ind ices on mi l l

feed

samples dur ing

these

s ix

months

ranged between

7.2

and 1 5.0 , but mainly between 10.5

and 1 2 . 7, averaging 11.6 . The mil l s

were es t imated

to be 20

percen t

i n e f f i c i e n t

as

measured

by

work

index.

I n co n s t r a s t ,

the

C i t i e s Serv ice

Pinto Val l

ey

opera t ion Gou

ld

, 1976) ,

u s ing s ix mil l s

of

the same s i ze as

a t

Bou

gainv i l l e

,

obta ined

an

i n i t i a l

13.2

p l an t work

index compared to an

or ig

i na l

labora tory

index

o f

12.8 .

Recent

opera t ions have

increased

d a i l y cap ac i t i e s

from

51,000

tpd

to

55 , 000 for one mon t

h ,

and

up

to

59,000

tpd fo r

a s ing le day Kennedy ,

1982) . These f igures show a s ub

s t a n t i a l decrease in the

p l an t

index

compared

to

l abora to ry f igures .

Gr i

nd

i

ng

Circ u

t Size

Dis t r i

but ions

Comparison o f

s i ze

d i s t r i b u t i o n s

fo r mi l l feeds and

cyc

l

one

underf l ow

c i rcu la t ing load) Table 1 ) go

fa r

toward expla ining the discrepancy

between

the

mil l s i

ndica ted

above .

These show c l ea r l y the tendency

o f

the

Bouga i

nv i l l e ore

to b u

i l d

up

in

the c i r cu l a t i n g load in

s i zes

above

6

mesh

-

58 percent

plus

6 m

esh

in

the

feed

and

-32

percen t

in the C.L)

with

the

weight propor t i ons

of

p l

us

6 mesh c i rcu la t ing l o a d ) / f e e d

about

32 x 4/58.

In

cons t ras t , the

Pinto

v a l l e y c i r cu l a t i n g load 5 . 5) shows

1 0 percent p l us 6 mesh , wh le new

feed has

51 percen t .

Grinding Kinet ics Factor

The

l

ower

r a t e

of g r ind

i

ng

fo r

coarse s i zes has a l so been

i l l u s t r a t

ed a t Bouga inv i l le

by calc

u l

a t ion o f

breakage r a t e co e f f i c i en t s Fig . 1) ,

with

s i zes

above 14 mesh B O ~ m

showing

decreas ing

coef f ic ien t s com

pared

to

f i n e r s i ze s . In

co n s t r a s t

,

s imi l a r

da ta fo r the

1 .7

x 1 . 5 m

5.6 x 4 . 9 f t ) p i l o t ml l s h ow no

decrease , bu t

cont inuing

inc rease

fo r

s i zes

coa rse r

than

14 mesh. Steane

and

Hinkfuss, 1976) .

A

more

d e t a i l ed

s tudy

o f coarse

p a r t i c l e gr inding k in e t i c s as a

funct ion of mi l l

d i

ameter

,

recen t ly

made ava i l

ab

l e

Kavetsky

and

Whiten,

1

981)

Fig.

2) ,

found t h a t

the m i l l

diameter e f f ec t i s not unique to

Bougainvi l le ores . The da ta a l so

show t h a t where

ore

gr ind ing

k i n e t i c s

are

s i ze

sen s i t i v e

,

the

e f f ec t i s

exh ib i t ed

i n mi l l s

above about 2.5 m

8 .2 f t . )

in

diameter

and

not

below

.

I t occu r s i n s i zes above 4 mesh

4 7 5 0 ~ m ) , diminishing wi th

s i zes

f i n e r than about 10 mesh 0 0 ~ m .


7/19

96


Table

1 . Screen

Analys is : Cumulative Percen t

Oversize

Pinto-Val ley*

Bou9:ainville**

Mesh

Microns

New

Feed

Cyclone

New

Feed

Cyclone

Tyler)

Underf l ow

Underflow

C.L)

C.L)

0

.50 in 12700 2.4

0 . 37l in

9423

7.

1

0 . 2

13

. 3

7.2

3 6700

27.4 2.9

4 4750 40.1

6 4 46.5

26

. 2

6

3350 50.9

1

0.4

sat

32

t

8

2360 59

. 0

14.4

65 . 0

37.7

10

1700

65 1

18.7

14 1180

71.5 25

. 2

74

. 3

50.1

20

850

75.9

33.0

28

600 80.0 44

. 6

79.8

65 . 3

35

425 82.7

58.5

48

300 85.6 74.9 84

. 6

81.2

65

212 87.6

83.2

100 150

89 . 6 88 . 9

89.1

89.0

150 1

06

91.2 92.1

200

75

92.6 93 . 9 94.0

92

1

-

200

7 . 4 6.1 6 0

7 . 9

100.0 1

00

. 0 100.0 1 00 . 0

Circu la t ing lo ad

r a t i o -

5.5

4 . 0

Data

from Gould 1976) **Data from Hinkfuss

1976)

t In te rpo

l a t ed


8/19

DYNAMICS OF LARGE GRINDING MILLS

497

z

0

,)

z

::I

...

z

0

t;

L J

..J

L J

Vl

1 0

0 .8

0 . 6

0 4

0 . 2

-+- 1 7 - m MILL

5.5 m MILL

150 600 2400

9600

PARTICLE SIZE

,

p m

Fig

u

re

1 . Se lec t ion

funct ion as

a func-

t i o n

o f p a r t i c l e

s ize

fo r

p i l o t

p l an t and l a rge - diameter ba l l -

m il l s . Bougainvi l le opera t ion

(Steane and Hinkfuss , 1979) .

Mill

Dynamics

Factors

The prev ious

di scuss ion

shows

c l ea r l y t h a t

the

l es se r

ef f i c iency

of the Bouga inv i l l e mi l l s i s

expla in

ed

by

r e l a t i v e l y

lower breakage

co e f f i c i en t s fo r coarse r

s izes

in the

plan t . The same

tendency

appears to

be presen t

i n

the Climax

2.74 m

( 9 f t )

and 3.86m (12.6 f t ) mi l l s , and

in

the

Mt. Lye

l l

3.05m (10 f t ) and

4.58m

(15

. 0

ft

mi l l s .

However

,

the

Pin to Val ley S.Sm

mi l l s

as

evidenced

by lack of bui ld- up

of coarse s i ze s

in

the c i r cu l a t i n g

l

oa

ds ,

and

by

a

lower

p l an t

work

in

dex compared to l abora to ry r e s u l t s ,

do not

show such

a tendency . Thus

the phenomenon i s s en s i t i v e to ore

breakage

c h a ra c t e r i s t i c s , as wel l as

to mi l l s i ze

and

p a r t i c l e

s ize .

The

fo l lowing quota t ion from

Taggar t (1927) both provides an

explana t ion and sugges t s a so lu t ion

to t he

problem: Davis

(1919) shows

t h a t the (proper)

speed of

the m il l

i s c lo se ly r e l a t ed t o the s i ze o f the

b a l l s ,

and

t h a t

the proper

co r re l a

t ion

i s

ind ica ted by the s iz ing t e s t

of

the re tu rn

sands from t

he

mi l l

c l

a s s i f i e r .

With

any

given

s ize

o f

b a l l , i nc rease in speed

r e s u l t s

in

decrease

in

coarse mate r i a l

in

t he

c l a s s i f i e r sands , i . e . , in inc reased

crushing

of

the coarser p a r t

o f

the

mi l l feed . . if the speed i s too

low,

t he

b a l l s ize being r igh t

fo r

the feed,

t he re i s

heaping

up of

mater ia l in

t he

coarser

s izes

of

c l a s s i f i e r

sand;

if t oo high heaping

up

in

the f iner

s i

zes .

E

E

....

E

.....

E

co

r

E

E

"'

"'

II

z

z

?

....

~

Cl

r:

.....

CD


9/19

98


This explana t ion and

the fac t s

on

whic h it

i s based , obta ined 60

years

ago,

are

in

agreement

with

the

fo l lowing t h e s i s : t h a t the p r in c ip a l

cause

of

the

Bouga inv i l l e

discrepancy

l i e s

in the

Q

/Qf

fac to r ,

which

var ie s

inve rse ly witfi d1ameter ,

reac t ing

with

Bougainvi l le

ore coarse

s i ze

breakage

chara

c

t e r i s t i c s . To

a

cons ide rab le

e x t e n t , as

a l r eady

p

ro

p

osed by

t he

Bougainvi l le

s t a f f , l e s s

favorable

mixing e f fec t s

may be involved , whi le

o f l e s s e r importance i s the reduced

r es idence t ime. However, lower

breakage co e f f i c i en t s t oge the r wi th

reduced r es idence t imes

compared to

smal ler

mil l s ,

may

i n t en s i fy

the

d i s

crepancy

.

Proposed Cor rec t ive Measures

The

evidence

presen ted i n d i ca t e s

the

bui ld up o f coarse r s i zes of some

ores

in

c i r cu l a t i n g loads

with

l a rg e r

mi l l s . This i s suppor ted by evidence

of decreased

coarse

s i z e breakage

ra t e

co e f f i

c i en t s again fo r some

but no t

a l l

ores .

A

so lu t ion

to the

problem,

where it se r io u s ly

a f f e c t s

mi l l pro

d u c t iv i ty ,

i s

in

the

d i rec t io n

of

inc reas ing ins tead o f

decreas ing

fc s

with

l a rg e r mi l l s . Before cons ide r ing

the d e t a i l s o f inc reas ing speeds two

ques t ions

must be r a i s ed .

l .

Can the ore p roper ty respon

s ib l e

be i d e n t i f i e d in

advance?

2.

What,

if any,

are the

pos

s i b l e s ide

e f fec t s

to

be

an t ic ipa ted?

Id en t i f i ca t i o n o f Ore

Proper t i e s

Pred ic t ion o f

coar se

p a r t i c l e

breakage ra t e decreases

i n l a rge m i l l s

in advance i s

a

d i f f i c u l t problem. t

obviously cannot be

accomplished

by

s tandard l abora to ry

b a l l

mi l l

gr ind

a b i l i t y t e s t s

us ing minus

6 mesh

feeds,

s ince it

only

a f fec t s s i ze s above

about

4 to 6

mesh, and i s found

only

in

mi l l s above m 9

. 8

f t ) in diameter

.

The problem i s

s imi l a r t o the accu

mulat ion of in te rmedia te s i zes in

autogeneous mil l s .

While no def in

i c :

so l u t i on

i s known

fo r b a l l

mi l l s ,

i s

poss i b l e

t h a t the competency t e s s

used

to

eva lua te

lump

ore

fo r auto

geneous gr ind ing

may

be

appl i cab le ,

MacPherson

and

Turner ,

1978)

o r

h e

a d ro p tes t ,

using

a

b a l l on plus 6-

mesh s i ze s ,

should be

used .

Side Effec ts

Bal l and

l i n e r wear

i s

t he ma jo=

unknown in i nc reas ing speeds

fo r l

~

b a l l mi l l opera t ion . Although e r l

~

work

c i t ed on ca t a rac t in g speeds re

por ted h igher s t e e l consumption

, th i s

preda ted

modern

a l loys for

b a l l s an

d

l i n e r s . t i s a l so l ~ k e l y t h a t

the

probable r educ t ions in volumes p a r t ic

u l a r l y in

co a r ses t

s i ze s , in c i r c u l

ing loads would have

a

r e l a t i v e

b en e f i c i a l

e f f e c t

on s t e e l wear . The

f ina l

proof must depend on t e s t i n g .

I f

speed

i s inc reased

to

o b ta i

n

the b es t opera t ing speed

BOS)

with

ou t dec reas ing the

load

f r ac t i o n ,

power

would

be

inc reased

by

about 20

percen t over

s tandard

condi t ions ;

t h i s i n tu rn would r e qu i r e

a

propor

t iona te

i nc rease in feed r a t e

to

mainta in t he

same

energy / ton , and

power e f f i c i en cy . Under t hese

condi t ions ,

however ,

feed r a t e i t s e l f

could

encounter

a

l i mi t a t i o n

before

ever

r each ing t he l eve l necessary for

cons tan t energy / ton

if

t he capac i ty

of the media

to

ax i a l ore

f low

i s

exceeded

Harr i s

and

A rb i t e r

, 1982).

The

mechanical

problems

o f

dr iv ing mi l l s a t speeds about 20 per

cen t h igher

t han

convent iona l

must

a l so be cons idered . Although opera

t i n g exper i ence wi th l a rge b a l l mil l s

a t such speeds i s

non-ex is ten t ,

much

l a r g e r

autogenous

and semi -

autogenous

mi l l s a re repor ted

to

be opera t ing a t

up to 90 percen t

of

c r i t i c a l , so

t h a t

no

insuperab le dr ive

problems

a re

an t i c ip a t ed

.

MacPherson and Turner ,

1978).


10/19

DYNAMICS

OF L RGE

GRINDING MILLS

499

Proposed

Opera t ing

Condi t ions

In broad

terms t he sca le -up of

opera t ing condi t ions

for

l a rg e r mi l l s

has u n t i l now been ch a rac t e r i zed by

the

two

co n s t r a i n t s :

1 . Use

of

cons tan t energy/ ton

[power / ton/hr ) ]

2. The progress ive reduc t ion

of percentage

c r i t i c a l

speed with

mi l l

diameter .

I s i s

now

proposed t h a t fo r ores

which show

lower

breakage ra t e s

in

coarse

f rac t ions

with

l a rg e r mi l l s

the second

cons t ra in t

should

be

reversed

, whi le

mainta ining

cons tan t

energy per

ton

by

i nc reas ing speeds

and

s imul taneous ly

reduc ing l oad

f r ac t io n s . t i s

fu r ther

poss ib le

to obta in a

load/speed

combinat ion

which

gives c lose

to

t he Davis

OS

and

t he

same r a t i o

of

ro t a t iona l

media f low to

pulp

flow

as in the

convent ional

combinat ion of load

and

speed

used

in

the

l a rge

mi l l s .

This

combination should produce

an

optimum

dynamic condi t ion

with

a

s u b s t an t i a l

degree of b a l l ca t a rac t i n g ,

t oge the r

with

t he loosening

and swel l ing

of

the load

to

br ing

l arge

b a l l s and

coarse

rock to the surface

o f

the toe .

This should break down

t he

coarser

s izes more

rap id ly

and with l e s s

f ine

product ion

Taggart

, 1927) .

The

capaci ty o f t he media

to

ax ia l ore

flow

wi l l

be

a

co n s t r a i n t

on

feed

r a t e which

should

be taken in to

account .

To obta in the

proposed optimal

condi t ions use can be made of : the

s impl i f ied power equa t io n ; the i n t e r

nal ro t a t iona l

flow

equa t ion appen-

dix)

and

the Davis equat ions. As an

i l l u s t r a t i o n of t h e i r ap p l i ca t io n

Figure 3 shows the equal

flow

and

equal

power

i n t e r s ec t i o n s

with

t he

Dav i s

OS

l i n e using t he base condi -

t ions :

L = 0 .

4 ; f

=

0.68 which r e f e r

to t he o ~ g a i n v i l l ~ o r i g i n a l operat jon.

able

2

compares power /capaci ty/ f low

f

igures

for

an 17.4

x 21

f t mi l l under

onvent iona l

opera t ing condi t ions with

0 90

u

0

0 80

ll

II

..J

ct

.)

t

0

70

BASE

a

CONDITIONS

.)

z

0

1

0 60

.)

ct

a

LL

0 5 0 L.....--..L.---...L.---- ------1

0 2 5

0.30

0

.3

5 0

40

0

45

LOAD

FRACT

ION Lt

Figure 3.

Davis b es t

opera t ing

speed

BOS) , equal power r a t i o

and

equal ro t a t i o n a l

flow

r a t i o

curves .

Lf

f

c

Base condi t ions

0.40

0 . 68

Davis

OS

and

equal

flow

0.31

0 .8 1

Davis

OS

and

equal

power

0.28

0 . 80

those es t imated

fo r t he

proposed

condi t ions .

t i s of i n t e r e s t t h a t the

Bougainvi l le

mi l l speeds

or ig ina l ly

a t 0.68 fc s

were increased to

0.71

in

1977

, with

seve ra l

mi l l s

opera t ing

a t 74 percen t

in

1980.

In

1982,

an

e leven th

mi l l

wi l l be commissioned

a t

82 percen t and a 12th a t

86

percen t

o f

c r i t i c a l

Mcivor, 1982).

However ,

i nc reases in

rpm without compensating

decreases

in load may

c rea t e

feed r a t e

co n s t r a i n t s

as

a l ready descr ibed,

and

it

i s

hoped

t ha t

t hese

w i l l be

inves -

t i g a t ed .

Summary

Evidence

i s summarized

to suppor t

the decreased e f fec t iv en es s

of

l a rg e r

diameter b a l l

mi l l s

fo r coar se p a r t i

c l e +6 mesh)

breakage with

some ores

.

This i s

r e l a t ed t o

decreased

media


11/19

5


Table 2. Operat ing Condi t ions:

Davis

BOS, Equal Power and

Equal Rota t iona l

Flow

(See Figure 3)

D x L ( l ) l

Lf

Load

N f

Qf(2)

p

QI

QI/Qf

I

Comments(

3

)

c

f t

St

rpm

s t / h r

HP

s t / h r

17. 4x21

I

0. 40 289.6

12

. 5 0.68

2415 4410

2.843xl0

5

117.7

I Base

Condi-

t i ons(4)

17.4x21

I 0.31 224.4 14.9 0 . 81

2564 4682 2.842xl0

5

110.8 I BOS and equal

ro t a t i o n a l

flow

17.4x21 I 0 . 28

202.7

14.7 0 .80

2386. 5 (

3

)

4358(

3

2

. 620xlo

5

109.8 I

BOS and

equal

power - equal

feed

(1)

Ins ide l i n e r s

(2) Mil l feed;

Qf/P 2415/4410

(3)

Discrepancies

a re due to

rounding

e r ro r s

(4)

Bougainvi l le opera t ion

(Harr i s & Arbi t e r ,

1981)

ro t a t i o n a l

f low/feed f lo

w r a t i o s with

in creas ing

mil l

diameter , and to con

t r i b u t i o n s

from

reduced mixing e f f ec -

t i veness and reduced

res idence

t imes .

Inc reas ing f r ac t io n c r i t i c a l speeds

toward

Davis '

BOS

with assoc ia ted

ca t a rac t in g , t oge the r

with

reduced

ba l l

loads , a re

suggested

as

co r

r e c -

t i v e measures.

Acknowledgement

Apprecia t ion

i s

extended to

the

Bougainvi l le Copper, Ltd. management

and s t a f f

for t h e i r

p

u b l i ca t io n s

which st imula ted

t h i s

study; to

Ci t i e s

Serv ice

Pin to

Va

l l e

y s t a f f

for

prov

id ing

much in format ion ; and to

R. E . Mcivor fo r he lpfu l

sugges t ions

about mil l speed i nc reases .

This work i s supported

by gr a n t s

provided

by Ci t i e s Serv ice co. We

are

g ra t e fu l fo r

t h e i r generos i ty

and

encouragement.

References

Arbi te r ,

N., and Harr i s ,

C.C

. , 1980,

En

e

rg

y and

Scale-up

Requirements

in Mineral

Process ing,

Fourth

J o i n t Meeting

MMIJ-AIME

Tokyo,

pp

63

-

83.

Davis , E.W. ,

1919,

Fine

Crushing

in

Bal l

Mil l s , Trans. AIME, Vol 61,

pp 250-296.

Gould , W.D . , 1976 ,

Pin to

Val ley

Concent ra tor Grinding with Large

Diameter Mil l s

, Trans. SME - AIME ,

Vol 260,

pp

268-274.

Hancock , R. T . , 1934,

Discuss ion o f

Bal l

Mil l ing

, Gow, A.M., e t a l .

Trans.

AIME, Vol 112,

pp

76-78.

Harr i s ,

c .c . ,

and

A rb i t e r , N., 1982 ,

Grinding

Mil

l

Scale-up

Problems,

Mining Engineer ing , Vol 34, No. 1 ,

Jan . pp

43-46.

Hinkfuss, D.A.,

197 6 ,

The

Bougainvi l le Copper Limited

Concent ra tor

Flo ta t i o n :

A. M.

Gaudin Memorial Volume,

M. C.

Fuers tenau,

ed. , Vol

2,

Chapter 40 , AIME, New York,

pp

1125-1144.

Kavetsky, A. , and Whiten,

W.J.

, 1981,

Scale-up

Rela t ions

fo r In d u s t r i a l

Bal l Mil ls , JKMRC Paper fo r

Aus t ra l a s i an

I n s t i t u t e

of Mining


12/19

DYNAMICS OF LARGE

GRIN ING

MILLS

5 1

and Metal lurgy, ( in pre ss ) .

Kennedy, A.J . ,

1982, Pinto

Valley

Concen t ra to r , (Pr iva te

communica

t ion ) .

Kjos,

D.M.,

1979,

Grinding

Circu i t s :

Current Sta tus

and Pro jec ted

Future

Development,

50th Annual

Meeting

of the

Minnesota Sec t ion ,

AIME,

Minnesota,

January 10-1 2 .

MacPherson, A.R. , and

Turner ,

R.R. ,

1978, Autogenous Grinding

from

Test

Work to

Purchase

o f a

Commercial

Uni t ,

Mineral

Process

ing Plan t

Design,

A.L. Mular

and

R.B.

Bhappu,

ed, Chapter

1 3 , AIME,

New York, pp 2

79-305.

Mcivor,

R.E.,

1981, The

Effec t s

o f

Speed and

Liner Configura t ion

on

Bal l

Mil l Performance, SME-AIME

Fa l l Meeting,

Denver, Colorado,

November 18-2

0 ,

p rep r

i n t

81-322,

pp 1-10.

Mcivor,

R.E.,

1982,

Pr iva te

communica

t i on .

Rowland,

C.A. ,

J r . ,

and Kjos, D.M.,

1978, Rod

and

Bal l Mil l s ,

Mineral Processing Plan t Design,

A.L.

Mular and R.B. Bhapp

u , ed,

Chapter 12 ,

AIME New

York, pp

239

- 278.

Steane, R.A., and Hinc kfuss ,

D.A.,

19

79

, Selec t ion

and Performance

o f Large Diameter

Bal l -Mi l l s

a t

Bougainvi l le Copper, Ltd . ,

Papua,

New Guin

ea ,

Proceedings of the

Eleventh

Commonwealth

Mining and

Meta l lu rg i ca l Congress,

Hong

Kong

1978,

IMM

London

,

pp

577

-58

4.

Taggar t , A.F. , 19

27

, Handbook o f Ore

Dress i

ng

,

Wiley,

New

York.

Taggar t ,

A.F. , 1945, Handbook o f

Mineral

Dressing,

Wiley,

New York,

2nd Ed.

Ti lyard ,

P.A. ,

1981,

R

ecen t Develop

ments in Grinding and

F

l o t a t i on

a t

Bougainvi l le Copper, Ltd . ,

Papua

New

Guinea,

Transac t ions ,

Ins t i tu t ion o f Mining and Metal

lu rg

y

(Sect ion C, Mineral Process

ing and Ext rac t ive Metal lurgy)

Vol

90,

pp

c

89-95.

APPENDICES

Power Consumption in Tumbling Mil ls :

Power Corre la t ion

Fac t o r

The load subtends h a l f

angle 6

a t

cen te r . Rota t ion

s h i f t s

the

load

through

ang

l e

a ,

which i s th

e

angle

o f repose

~

. .

o ,

' /

/

. l

/

-------.._. ....-...- ----

/

/

'

,

G

w

Weight

o f charge:

W

2

rrp LD

Lf/4

Load

f rac t ion : (6-

s in 6c os

6 )

/rr

(2 6

- s in2

6 ) /2

Center of grav i ty : t h i s t rea tment

does

not

take

account

of the

d i f f e r en t

bulk

dens

i t i e s of the

ascending

and

descending

media

flow

paths ,

nor the p i l ing-u

p

o f

the media a t

3

the

toe .

OG = OG' = Dsin 6/3 ( 6

- s in

6

cos

6 )

= Dsin3 6 /3rrLf

Torque : T = Wg OG ' s in a

Expe r imentat ion

sh

ows

t h a t

mo dera te speed changes

do not

a f f ec

t

t o rqu

e

very much.

Power

: P = 2 TN

There are

severa l

a l t e r n a t i v e


13/19

5 2


express ions

for power depending on

the v ar i ab l e s chosen to express mi l l

opera t ing

parameters . Two

examples

a re :

p

2DNWgsin

3

6

s ina ) /3Lf

(

rr

pgNLD

3

s in

3

6s in a

) /6

An approximat ion to

Sin

3

e i s

4L

1-Lf) . The

fo l lowing

t ab l e shows

gooa

agreement

over the t y p i ca l opera

t i n g

range

Lf -

0.3S to 0.4S

.

Lf

Sin

3

6

4Lf l -Lf )

0 . 30

0.8Sl

0.840

0.3S

0 .

917

0 .

910

0.40

0.963

0 .

960

0 .

4S 0.991 0 .990

0 .

50

1 . 000

1.000

Using

these values

, a

use fu l

cor re la t ing equat ion

i s

P / W N D l - L f )

S g s i n

When W i s in

shor t

tons , N in

r .p .m.

,

Pin H.P. , and D i n f ee t

the

equat ion

becomes

P / W N D l

O . l 6 1 6 2 s in

a

Three

values

o f

a

quoted in

the

l i t e r a t u r e , and

the cons tan t on the

r i g h t hand

s ide

o f the above equat ion

are :

a

Constant

All is -Chalmers

slowspeed)

43

0.11022

normal mil l s )

SID 0 .

12S6

Hancock

sao

0.1371

Be c

ause

manufac turers

o f

l a rge

diameter

mi l l s reduce the f rac t ion

c r i t i c a l speed

as

diameter

inc reases

it i s convenien t

to

cor re la te

mil l

da ta

according to P/WND l-Lr.)

versusD

.

Various manfacturers

es t imated

power

requi rements

are shown in

Figure

Al.

Equal-Power

and

Throughput Ratio

I f a mil l i s

opera ted

a t

speed

N

1

fc , l ) and load

L f , l

and then a t

new speed N

2

fc ,

2

) and load L f,

2

othe r

th ings

being

equal , the

power

consumption

and th roughput

wil l remain

unchanged if

f / f

c l

c ,2

Nl/N2

L f , 2 l -L f , 2 ) / L f , l

l -Lf , l )

In t e rn a l Rotat ional Mass Flow

Harr i s and Arbi te r ,

1982)

From

dimensional cons ide ra t ions ,

the

ro ta t iona l

mass

flow

QI

i s

r e la ted

to the mi l l

ro ta t iona l

speed , N; mil l

diameter ,

D, and

l eng th ,

L,

by con

s tan t

dimens ionless

f low

number,

NQ

QT/NLD

2

. Th us ,

sp ec i f i c ro t a t i o n a

l

flow

(

flow

per u n i t volume)

i s

propor

t iona l

t o mi l l ro t a t i o n a l speed , and

because

N

decreases

with

i nc reas ing

mi l l

diameter

roughly

according to

N ~ o-O . S) it fo

ll

ows

t h a t

sp ec i f i c

ro ta t iona l flow diminishes

with

in

creas ing

mil l diameter according to

- 0 .

s

th .

f .

D .

Because

bo

s p e c ~ ~ c

power

and sp ec i f i c th roughput i nc rease with

inc reas ing

mil l diameter according to

0.5 . 1

D , the

s t rong

~ n v e r s e

sea

e -

up

r e l a t i o n sh ip s

:

QI/Qf D-

1

; QI

/P

1

D :

are ev iden t .

An

an a ly t i ca l

express ion

for

QI

in terms of

the

mil l parameters may

be

der ived

by i n t e g ra t i

nc

t

mass flow

along annular r ings with in t he r o t a

t i ng charge.

A

s impler approximate

method

based on

the

torque-arm

model

wil l be

given

here , which i s adeq

ua t e

fo r use with

i n d u s t r i a l data .

Q

would assume

its

minimum

value

i f

the icharge were d i s t r i b u t e d evenly

around the

she l l

and

then ro ta t ed

with

the sh e l l witho

u t s l i p . I f

t he weight

of

charge

i s

W then

2

QI = W = rrD

LPNLf/4 .


14/19

0.15

0

z

31:

......

0.14

0..

0

1-

0 .13

u

ct

...

z

:?

0 .12

1-

ct

...J


15/19

5 4

DESIGN INST LL l iON OF

OMMINUTION

CIRCUITS

At the

o ther ex t re

me ,

the

max

imum

value o f Q would occur

if

the

charge

were fasfl ioned in to a cy l inder

of

diameter ,

d , and

length ,

L , ro ll

ing

without s l i p i n s ide

the

she l l

then

QI

2

WND/d = WN/Lf

2

0 . 5 /

D LNLf 4

A

model in te rmedia te

between t he

above two

i s

provided by the

media

conf

i gu ra t ion

assumed in the torque

arm

mode l

[per imeter

= (8+sin 8 )D)

der iva t ion o f power .

Again

, assuming

ro l l ing

w

i th

o

u t

s l ip

,

QI

nWN/ (8+sin 8 )

n

2

D

2

LpNLf/4( 8+s in 6 )

Comparing the

t h ree models

in

terms

o f the

Q

1

/WN

r a t i o : Mode l 1 , Q /WN=l ;

Model

2,

Q

1

/WN=L- 0 .

5;

Model 3 I

Q

1

/WN

=n / 6+sin 6 ) . Comparat ive va l ues

fo r

the

normal range

o f

Lf

are

given

in the Tab l e Com

pa

r i son o f Models

The inc rease in

Q from

~ n ~ u

to maximum (m

odels

1

afld

2 respec

t ive ly )

i s

only

o f

the order

o f

50

to

70

, while

the value given

by

m

ode

l 3 i s almost t h e averag e o f

mode

l s 1

and

2 .

The

equa t ion fo r i n t e rn a l

ro t a t i o n a l

mass

f low

in

convenient

un i t s

i s

Q

1

s t /h r ) : l 88.5W(s t ) N (rpm )

/ (8+

s in 6 )

Equal

In

t e rn a l

Rota t iona l Flow

Rat io

I f a m il l i s opera t ed a t speed

N

1

(fc ,

l )

and

l

oad

Lf

, l (6

1

) , and

then

a t new

speed

N

2

(fc ,

2

) and l oad Lf ,

2

(6

2

) , o ther th ings being equa l ,

the

i n t e rna l r o t a t

i ona l flow wi l l remain

unchanged

if

fc , l / f c , 2 = Nl /N2

= Lf ,

2

(8+sin6)

1

/Lf ,

2

(6+s in 8 )

2

Comparison o f Models

1 2

3

average

Lf

1

Lf

1

n / 6

+s in 6 )

1

and

2

0 .

35

1 1 . 6903 1 . 364 1 . 3452

0 . 40 1

1.

5811

1 .

3085

1 . 2905

0.45

1

1. 4907

1 . 2607

1 . 2454

Note: Dav i s

(1 919) gives 1.44

cyc les o f charge

per mil l

revo

l

ut ion

a t proper

speed.


16/19

DYN MICS OF

L RGE

GRINDING

MILLS

Table Al.

i l l

Loading: Manufacturers Recommendations

Al l i s - Chalmers:

All mi l l s ,

Lf

- 35-45

All

mi l l s ,

Lf

-

45

Marcy: Rod mil l s

and

wet gra te ba l l mi l l s , Lf 45

Denver:

Wet overf low

ba l l

mi l l s

40

Nordberg: Rod mil l s ,* Lf

=

32-40 ; Bal l mi l l s , Lf ~

Smidth : Wet overf low

rod mil l s , Lf 40

;

All

o the r

mi l l s ,

t

Lf

35

* T

hese

loadings

expand to 40-50

dur ing opera t ion.

t Wet ove r f low ba l l

mi

s ,

wet

pebble

m il

l s ,

wet

autogenous and

semi- autogenous m il l s .

Table A2.

Grinding Media Data

(S

t e e l

de

n

s i t y

-

490

l b

s /cub

ft

Mil l

Diameter

Densi t

y

Voidage

f t )

(l bs/cub f t )

(

percen t )

New r ods

390

21

Wo rn - in

charge

3- 6

36 5

25

6- 9

360

27

9-12

350

29

12- 15 34 0

31

Bal l s

290

41

Taggart

5-32)

304

38

5 5


17/19

5 6


Tab l e A3. Pulp Spec i f i c Gravi ty

Sol ids by

weigh t I

Dry

Ore

Sp Gr

(percent)

2.2

2.6

2 . 8

3.0 3.2 3 .4 3 .8

40

I

l 28

l 33 l 35 l 36 l 38 l 39 1 .42

s l

38

1.44 1.47 l

s

1.52 l 55 l 58

60

I

l 49 l 59 1.63 1 .67 l 70 l

74

l 79

70

I

1 .6 2 l 76

1.82

1.88 1 .93 1 .98

2.07

80

I

1.77

1.97

2.06 2.14

2.22

2 . 30 2.44

Table A4 .

Average

Recommended

Operat in g

Speeds

(Percent Cr i t i ca l

Diameter D

f t

I

Rod Mills Bal l Mil ls

l l is -Chalmers Marcy

Smidth

All is -Cha l mers Marcy

Lf - 35-45

45

40

Lf-35-45

40

3- 6

76

-73

75 80 -

78 79-78

6 - 9

73-70 73-67

75

78-75

78-75

9-

12

70-67 67-63 73-71

75

-

72

75

-

73

12 - 15

67-64 63

- 61

69

- 68

72-69

73 - 71

15-18 69

-

66

71-70

18-21

Denver

Rod Mil l s : 3- 6 f t , 72-70 ; 6 -7 f t , 70-69 ; 8-10 f t , 65-58

Bal l Mi l l s

:

3-10 f t

, -75

t

Smidth

35

78

78-76

76-75

75-74

74-70

Marcy recommends

t h a t

rod

m i l l

speed

should

be determined

by per iphera l speed,

not percen t

c r i t i c a l speed : speed f .p.m. = 2SOD0 . 3

t

Marcy recommends

tha t :

b a l l

mil l

percen t

c r i t i c a l

speed

=

93D

- O. l

All is -Chalmers da ta gives f fo r m il l s D9

c c

Notes

Smidths

speeds are the

highes t

in

both

ca tegor ies .

All is -Chalmers rod

m i l l

. speeds are higher

than

Marcys but t h e i r

l a rge b a l l m i l l speeds are cons iderab ly lower . The Bougainvi l le

exper ience sugges ts t h a t the speed o f

l a rge

mi l l s could be

increased

with

advantage in inc reased throughput .


18/19

DYN MICS OF

L RGE

GRINDING

MILLS

5 7

Table

AS

Mil l

Type :

Relat ive

Power Requirements Based

on Wet Overflow

Ba l l Mill *

Bal l

Mil l s

Rod Mil l s

Wet Wet Wet

Dry

overf low

Wetgrate

Drygrate

overf low

pe r iphe r a l

pe r iphera l

Nordberg

1 1

13

1 25 1 1 0 1

24

1

37

Al

l i s

- Chalmers 1 1 1 6

1 08

* It i s

poss ib

l e to compare

the recommended

opera t ing l eve l s of di f fe ren t mi l l

types under otherwise i den t i ca l condi t ions in

few

cases

T

ab

l e A .

Rod Mill Grinding Media Expansion Due to Rotat ion

Percen t c r i t i c a l

speed

f

0

50 60

70

80 90

c

Mil l

l

oading percen t

Lf

45

. 0

55 5 57 5

59 . 5

61 5 63

. 5

Media voidage percen t

E *

21 0 36 . 0

38 2

40 . 3

42 2

44 . 0

LfE

9 . 5

20 0 22 . 0 24 . 0 26 0 28 . 0

Table A7 . Grinding Media Expansion : Ball Mil l Media Voidage

Mil l load ing percen t

45

50

Media voidage percen t

E * 41

46 9

Sta t ionary

va l ues : Lf 45 , E 41

*E [Lf - so l i d volume/mi l l volume ]

/Lf

55

51 7

28 . 5

60 65 70

55 8

59 . 2

62 1

33 . 5 38 5 43 5

95

64 5

44 . 9

29 0

75

64 6

48

. 5


19/19

5 8


Tabl

e

A8. Notat ion

D Mill

diameter

measured i ns ide l i ne r s

f

Fract ion c r i t i c a l speed

=

NJD/76.63 where

N

s n

r pm

and

D

n

fee t

c

L

Mil l length measured in te rn

a

y

Lf

Loading: f r a c t i

on of

mil l volume occupied by gr inding

media,

me asured

a t r e s t

N

Mil l

ro t a t iona l

speed: revolu t ions

per un i t

t ime

n Average

number of revolu t ions during the

res idence

of

an

element

of

ore

n

the

mil l

=

Nt)

P

Mil l

power consumption:

ne t

power =

consumed

power - id l ing

power

Qf

QI

t

v

v

m

v

p

w

t

e

6

p

CJ

T

Mass feed r a t e of ore through mil l : ax ia l mass f low

r a t e

0 5

[=new feed r a t e x 1 + c i r c u l a t i ng load r a t i o . Note: Qf/V D ]

Mass

ro t a t iona l

f low

r a t e : may r e fe r to s t e e l ,

o r pulp, o r

dry ore ,

o r any combination , depending on densi ty te rm, p Q pNV

Note:

Q ; v ~

0

-0 .5

I m

Nominal

residence

t ime o f or

e

element n mil l

= Vpcr

/Qf)

Mil l volume

=

Volume

of mi l l occupied

by media =

VLf)

Volume

of

pulp =

Vm

e )

Weight o f mil l

conten ts :

may

r e f e r

to

s t ee l or

pulp or dry ore

depending

on densi ty term,

p =

Vm

p )

Angle of repose

Grinding

media void ra t io : void volume/bulk volume e - 0.41, new b a

charge;

e -

0.38, seasoned ba l l charge Taggart

5-32); e -

0.4

to

0.6 ,

expanded due to mil l r o t a t i on

Autogenous mil l s : e =

1;

e

=

1 .2 ,

expanded due to mi l l ro ta t ion

Half

angle subtended a t

mil l cen ter by gr inding

media

a t r e s t

[

6 - s i n c o s / ~ = Lf]

Densi ty

of

mil l

conten ts o r o f

a component

of conten ts :

bulk

densi ty

of

ba l l

load

- 290

lbs /cub

f t ;

s t ee l densi ty

480

lbs /cub f t

Ore densi ty

Tor

q

ue

Scale-up and Dynamics of Large Grinding Mills - A Case Study

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Transcript of Scale-up and Dynamics of Large Grinding Mills - A Case Study