THE TOOLS OF POWER POWER: The Bond Work Index, A Tool To Measure Grinding Efficiency C. A. Rowland, Jr. Senior Process-Project Engineer /-. - Yining Systems Division , IJ Allis-Chalmers Corporation - - Milwaukee, Wisconsin . , - - ... , For presentation at the 1976 SME-AIME Fall Meeting & Exhibit Denver, Colorado - September 1-3, 1976 PREPRINT NUMBER 76-B-311 .mi . A1 ,?Em - % 4c
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THE TOOLS OF POWER POWER:
The Bond Work Index, A Tool To Measure Grinding Efficiency
C. A. Rowland, Jr. Senior Process-Project Engineer /-. -
For presentation at the 1976 SME-AIME Fall Meeting & Exhibit Denver, Colorado - September 1-3, 1976
PREPRINT NUMBER
76-B-311 .mi . A1 , ? E m - % 4c
-1-
~ D U ~ ~
With the rapidly rising cost for electrical energy and the long range pre-
dictions for continued rising costs and ewn possible energy shortages, operation
of rod, b d l , autogenous and partial autogauxls grinding circuits to efficiently
u t i l i ze the pwer delivered to the mills w i l l be a d e d . This calls for a wthod
to evaluate grinding circuit: p e r f o m c e that is accurate, reliable and readily
usable as an operating tool by supervisory, technical and operating personnel.
Neither the Rittinger a d Kick theories of camhution, which preceded
the Bond Theory by m r e than 50 years, had a mthematical mans that could be
used to predict and evaluate the perfonrwce of crushers and grinding mills used
to comninute ores and rocks. This severly Limitd the practical use of these two
theories, whichmre confzadictory to each other. They have been superseded by
the Bond Third Theory of ccminution. (1)
DISCUSSION
In addition to the Third Theory of 'kminution, better known as the Bond
Theory, Red Bond mde three significant contributions to ass is t in the efforts
t o change the art of cominut ih into a science.
1) The Bond rod milling and ba l l milling closed circuit grindability tests.
2) The Bond impact crusher tes ts .
3) The Bond equation, the mathematical statemnt for applying Bond Theory
of Comminution. (1)
Where W = Wk hrs. per short ton (907.44 kilograms).
wi = iyrork Index
P = Product size in m i m e t e r s which 80;L passes
F = Feed size in m i c m t e r s which 8VL passes
Power per metric tome (1000 k i l o g r m ) can be obtained by multiplying W by 1.102.
Grinding power calculated, h e n using work indices obtained from Bond
- 2- (2)
grindability tests in the Band Equation, is for the follu~iTlg specific conditions:
1) Rod Ni.lling - wet, open cikcuit grin- in a 2.44 lrrter (8') dianrter
inside liners rod m i l l .
2) Bdll Nilling - wet closed circuit grinding in a 2.44 naeter (8') W t e r
, inside liners bal l m i l l .
3) P a ~ e r calculated is the p w e r required a t the pinion sha£t of the mill ,
which includes m i l l bearings and gear and pinion losses, but does not
include m t o r losses o r losses in any other drive cmpments, such as
reducers and clutches.
There are eight efficiency factors that are applied to the calculated grind-
ing p u m to a l l m for variations fram the specified conditions as related to the
grinding circuit and equipznt used. The background and reasons for these have
been published ( I ) , (2), (3) and are not part of the discussion. The factors are:
EF1 Dry Grinding
EF2 Open Circuit Bdll Milling
EF3 Di-ter Efficiency Factor
EFq Oversized Feed
EFj Fine grinding in bal l mills to product sizes finer than 8U77 passing 200
msh (75 microueters)
EX6 High or IWJ ra t i o or reduction rod milling
EX7 LorJ Ratio or reduction bal l milling
EF8 Rod Hilling
When accurate, Mill Feed Rate, M i l l Parer , Feed and Product Size Analysis
data are available, using the Bond Equation as shown, m r k indices can be calcula-
ted. To distinguish these fnrm ~mrk indices (ITi) obtained from grindability tes ts
~urk indices calculated frm operating &ta are designated as !.Jio.
In using this equation, the feed is the feed to the grinding circuit and the
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product is the product fran the circuit. In a closed circuit operation, do not
use the f e d into and the discharge from the mill as is done with an open circuit
mill. Work index is a ueasure of grindability for the work to be done o r dune in
grinding the circuit feed t o the circuit product.
Operating rark index has the sane definition as ' tmk index1'(') which states
that "wrk in& is the required to break a hnmgenous material from a
theoretically infinite feed size to 8W0 pass- 100 micrmters". Thus, by defi-
nition, wrk indices calculated fran operating data always relate the operating
Qta fram which Wio is calculated, to the s a m feed size and product size as
giwn in the Mini t ion ; n a ~ l y , f rom a theoretically infinite feed s ize to 80??
passing 100 m i c m t e r s .
Thus, operating rmk hdex can be used for in-plant grinding mill reporting
and grinding studies such as :
I) Record m i l l p e r f o m c e on an hourly, daily, weekly or m t h l y basis,
whichever is desired.
2) Ccqare current p e r f o m c e with past p e r f m c e .
3) Cornpare c'kcuits in a d t i - c i r c u i t plant.
4) In plants ~$-ith two or mre grindjng circuits, one or m r e circuits can be
used as a standard, with others as tes t circuits for testing the effect
of such variables as:
a) dl1 spee&
b) size of grinding media
C) feed size
d) product size
e) ~ n x r n t of grinding mdia in m i l l
f ) liner designs
g) liner wear
h) changes in ore .
5) ikasure grinding efficiency.
GRINDING EFFLCIENCJ
As calculated, operating work indices include mto r , drive knd grinding m i l l
efficiencies and inefficiencies, therefore, are not directly comparable t o mrk
indices obtained from grindability tes ts performed on the same m i l l feed, without
the application of correction factors.,
M i l l parer as m u r e d in many p lmts is m t o r input pmer, that i s , electri-
cal energy going into the w t o r . It has to be converted to power a t the m i l l
pinionshaft. This is done by applying the m t o r efficiency factor (electrical and
mchanical losses) to obtain w t o r output pwer. I f the plant does not have the
w t o r efficiency data, it can be obtained £ran the m t o r mmfacturer. When the
mto r i s coupled direct t o the pinionshaft, notor output pmer is m i l l pinionshaft
power. I f a speed reducer or other drive element i s used between the m t o r and the
pinion shaft, then the efficiency of the units used must be applied t o the mtor
output power to obtain pwer a t the m i l l pinion shaft.
The grin- efficiency factors should be 'applied as required t o place the
operating work i n d e ~ a t the same level as the results from grindability tests. The
operating work index so calculated is referfed to as Wioc. This operating work ,
index divided by the mrk index fran the grindability tes t gives a reasme of ,
grinding efficiency as a d t i p l i e r of grindability tes t results.
f ~ ) = Efficiency Factor
The efficiency of the grinding circui t is
100 [L) = -ding efficiency in percent wioc
The multipliers for the efficiency factors can be determined from the f01lm-k~:
EF1 - Dry grinding - for the same range of work as wet grinding, dry grinding
requires 1.3 tines as m h pmer as wet grinding.
EF2 - Open Circuit Grinding - when grinding in open circuit bal l mills, the
amunt of extra power required, compared to closed circuit bal l milling,
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is a function of the degree of control required on the product produced
The inefficiency factors for open circuit grinding are given in Table I.
EF3 - D b ~ ~ t e r Efficiency Factor - using the base m i l l h t e r of 2.44 mters
(8') inside liners, the W t e r efficiency factor can be calculated
fran the following:
(4)
Table I1 gives a tabulation of EF'3 factors for some of the m r e comrpn m i l l
m t e r s in both the imperial and mtric measuring systems. This table S ~ J S
that when the m i l l d i a ~ t e r inside liners is larger than 3.81 ~ t e r s (12.5 ') that
the d.izmxer efficiency factor does not change and remains 0.914.
EFq - Oversized Feed - when the grinding m i l l is fed a coarser than optirrnrm
feed, this factor applies to rod milling and ba l l milling. The wst
frequent use is with single stage ba l l milling. This is the one
efficiency factor that is directly related to work index as is s h m in
the following equation:
Where Rr - Ratio of reduction = F H
(6)
Fo = Optiwrm feed size (7) Rod milling: 16,000
When available, use the mrk index fran a grindability tes t a t the desired
grind for Wi in equation 5. For equation 7 , if available, use either the work .
index from an impact t e s t o r a rod m i l l grindability test , xhich ever is higher
and for equation 8, use the work index from a rod mill grindability tes t , since
these m e represent: the coarse faction of the feed which is the portion of the
f&d coarser than optiuium. Tf not available, then use the grindability tes t re-
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sults , available.
Without grindability tes t results, finding the proper work index figure to use
in equation 5 i s a trial and error calculation which can be p r o g r m d for a am-
puter. Using this approach, the nark index used in equation 5 should equal the
Wioc obtained, after applying EFq and al l other correction .factors t o the mrk
index calculated from operating data.
EF5 - Fineness of Grind Factor - chis applies to fine grinding when the 8VL pas-
size of the product (P) is finer than 75 miaomters (200 msh). The equa-
tion to determine this is:
EF6 - High or Low Ratio of Reduction Rod f i l l ing - the equation t o be used, un-
less :
L = Rod Length
This factor generally applies to low ratios of reduction, but its applica-
tion to high rat ios of reduction does not always apply and should be used
only if the Wioc i W i grinding efficiency factor indicates that it should be
used.
EF7 - Low Ratio of Reduction Ball M i l l - the need t o use this factor does not
occur very often as it only applies t o bal l milling when the Ratio of Re-
duccion is less than 6. This sham up p&ticularly in regrinding concen-
t rates and tailings. The equation for this i s :
EF8 - Rod Milling - a study of rod m i l l operations shows that rod m i l l perf-ce
is affected by the attention given to feeding a uniform feed size t o the
m i l l and the care given t o maintaining the rod charge. This efficiency
factor cannot be definitely determined. In selecting rod mills based upon
pmer calculated from grindability t e s t s , the following procedure has been
recomnmded (2) :
1) Idhen calculating rod m i l l power for a rod-ailling-only application, use
an inefficiency factor of 1.4 when the feed is to be prepared w i t h open
ci rcui t crushing, and use 1.2 h e n the feed .. is to be prepared with
closed c i rcui t crushing. The other milling efficiency factors also
rmst be applied t o the calculated. grin- power.
2) !hen calculating rod m i l l power for a rod mill-ball m i l l c i rcui t , do not
allm for i m p r m w t in the ba l l mill performance. I f the rod m i l l
feed is produced w i t h open ci rcui t crushing, apply a 1 .2 inefficiency
factor t o the pier calculated for the rod milling stage only. If the
rod m i l l feed w i l l consistently be 80"/. passing 1/2" o r finer, such as
produced with closed c i rcui t crushing, do not apply a rod m i l l ineffi-
ciency factor. The other milling efficiency factors also m t be
applied t o the calculated grinding p-.
While this factor i s used in selecting rod mills, the inabili ty to ma-
sure and define i t accurately reduces i t s value and significance in
calculating Wioc and therefore, should probably not be used in deter-
mining the efficiency of rod m i l l performance, However, hcwledge of
its existence can be helpful in analyzing rod m i l l p e r f o m c e .
MAMPLES
The f i r s t ~ W O exanples are given to show haw to calculate W i o and Wioc for
single stage ba l l mills. Figure 1. The f i r s t example is a couparisun of bm
parallel mills frcan a daily operating report. P i i l l s ize 5.03111 x 6. lm (16.5' x
KwHfi4tric tonne
W i l l 1 M i l l 2
10.8 11.3
Feed s ize (8W7 passing) nicraneters 7500 8600
Product Size (80'77 passing) micrometers 220 195
Calculated Work Index Wio (Equation 2) 19.33 18.58
Correct t o Pinionshaft Power Wtor 18.56 17.84 Efficiency 0.96
Convert t o Short Tons Nil t ip ly by 0.9074 16.83 16.18
D i i m e t e r Efficiency Divide by 0.914 (m3)
Ball mi l l grindabili ty t e s t a t 65 resh gave a W i - 14.5. Using this t o
calculate oversized feed factor:
E q = (See Equation 5) =
Divide by EFq
Wioc
Efficiency Factor = & =
W i
Efficiency in % 96 99
This example shows that M i l l 2 is sl ight ly m r e eff ic ient than M i l l 1 even I
though it has a higher pawer consumption per tome. This shows the use of the
mrk index equation taking into account the differences in feed and product sizes.
The calculation is only pa r t of the t o t a l plant performance study and must be I tied into the to ta l plant operation.
The next sample covers an in-plant study on the effect of mi l l speed on
m i l l performance. The two speeds being studied a re 68"/, and 73% of c r i t i c a l speed I in 5.03111 (16.5' d i e t e r inside she l l 16' inside liners) b a l l mills. This study I was over a period of four m t h s . Grindability t e s t s were nm on m t h l y coqxsite
samples of the feed t o each m i l l . The operating data, t e s t data and calculations
are given in Table T I I .
The data given in Table I1 can be campared in several ways. A cmparison
based upon pawer per ton cons~led is given in Table IIIA. This shows the differ-
ence in p e r per ton of mi l l circuit feed cormm~d without taking into account
the variations in mi l l c i rcu i t feed, mil l c i rcu i t product and grindabili t ies as
shown in data tabulated i n Table 111.
E l k b a t i n g variations in mill c i rcu i t feed and product, Table IIIB shows
the comparison based upon the w r k index calculated fkom the operating data (Wio).
The next comparison eliminates the variations caused by differences in the
grindability of the ore. This i s the unre accurate comparison as it compares
grinding circuit p e r f o m c e as referred t o a comrpn base or reference. Table
I I I C gives the comparison based upon Wioc. - W i
The next two exarples a r e fo r rod m i l l ba l l mi l l circuits. Figure 2 shars a
conventional rod mill-ball m i l l circuit. The data fo r this circuit and \Jio calcu-
lations are:
Rod mil l s ize 3 . h x 4.88m (11.5' x 16' diarneter inside shel l 3 . 3 5 ~ 1 1 '
4.72111 15.5' rods)
Ball m i l l s ize 4.7211 x 4.88m (15.5' x 16' cLim~ter inside she l l 4 . 5 7 ~ 1 5 ' )
Rod m i l l feed produced by closed c i rcu i t crushing mimanzters 14,500