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• Tsakalakis G. Konstantinos

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(a) Three 4,400 hp. 14' x 38'7" Nordberg Ball Mills with trunnioncoupled speed reducer drives and one 1750 hp, 14' x 21 '2" Rod Mill , grinding taconite {b) Six 12'6" x 25'6" Nordberg Pebble Mills grind ing iron ore (c) Thirty-eight 12' 2" x 15'4" Nordberg Rod Mills and thirty-eight 12' 2" x 14'6" Nordberg Ball Mills installed in a tacon ite concentrator. (d) 10' x 33' Nordberg Ball Mill with trunnion-coupled speed reducer drive, grinding cement clinker {e) Two 1900 hp , 14' x 20' Nordberg Rod Mills and four 2000 hp. 14' x 22' Nordberg Ball Mills grinding taconite (f) Four 1250 hp, 12'6" x 18'6" Nordberg Rod Mills and eight 1250 hp, 12'6" x 15'6" Nordberg Ball Mills installed in a copper concentrator (g) Fi ve 2500 hp, 12' x 36' Nordberg Ball Mills installed in a wet process cement plant

2

0

1971 , Nordberg- Division of Rex Chain belt I

The term "grinding", as used in this bulletin, refers to the size reduction of material by tumbl ing it, together with media, in a rotating horizontal cylinder. The media may be steel balls , rods or rock pebbles. Energy is consumed in keeping the mill and media in motion; part of this energy is used to perform the useful work of breaking the material which surrounds the media. This method of size reduction is statistical in nature. The feed material will have a particle size distribution which normally follows a certain pattern . When this material is fed to a mill, there is a probability that any given piece will be broken up. The problem in designing a grinding circuit lies in selecting conditions which increase the probabilities of breaking particular sized particles to produce the desired product size distribution. This must be accomplished at the optimum combination of capital and operating costs. These costs, together with expected productive availability and total service life, comprise the factors which determine grinding machinery's contribution to profit. Nordberg's design and manufacturing goals are to produce grinding mills which will return a maximum profit to the customers' operations. Nordberg Rod , Ball and Pebble Grinding Mills are built to meet specified cond itions for wet or dry gnnding in the manufacture of cement , the fine reduction of metallic and non-metall ic minerals and other processes where material must be comminuted to fine sizes. No one is better equipped than Nordberg to produce the extra-large grinding mil ls wh ich increase production most profitably. Some of the largest mills bu ilt in recent years have emerged from Nordberg 's excellent manufacturing facil ities. In order to assist in the selection of the optimum type and size of grinding machinery for a particular installation, Nordberg maintains a test facility in which grindability tests, actual production runs and other testing procedures are conducted. These facilities, and the abilities and knowhow of a professional research staff, are made available to every potential purchaser of Nordberg Process Machinery (see page 20).

contents In addition to providing a good deal of information about the design and construction details of Nordberg Rod , Ball and Pebble Grind ing Mills, this bulletin includes step-by-step procedures to be used in determ ining horsepower and mill size requirements for a specific application. The dimensional data at the end of the bulletin will enable the reader to make a reasonab ly accurat~ preliminary plant layout, once approximate motor and mill size have been determined .

SELECTING A GRINDING MILL Grinding Mill Types: Rod Mills . ... .... . . . . . .... .. ... . .. .. ... p. 4 Ball Mills .. .. .. . .... . .... . ... ... .... pp . 4-5 Pebble Mills . . .... . ... . . . .. . . . .. ...... . p. 5 Wet vs Dry Grinding . .... .. . . .. .... .. . . . .. p. 6 Grinding Media: Charge Volume . . . .... . . ... . .. . ... . . . pp. 6-7 Media Size . . .... . . .. ... . . .. .. . . .... pp . 7-8 Consumption of Media ..... .. .. . . ....... p. 9 Calculating Motor and Mill Size : Determining Horsepower Requirement .. pp . 9-10 Matching Mill Size To Horsepower Requirement .. . ..... . ...... . ..... . pp. 10-12 Capital Costs and Operating Costs .... . .... p. 12 Large Mills vs Small Mills . . . ...... . . . ..... p. 13 NORDBERG GRINDING MILLS : General Description ......... ... . ... .. pp . 14-15 Details Of Various Parts And Assemblies pp . 16-19 RESEARCH, DEVELOPMENT AND TESTING . . p. 20 ROD MILL DIMENSIONS AND WEIGHTS . ... p. 21 BALL MILL DIMENSIONS AND WEIGHTS pp. 22-23

grinding mill types The type of grinding mill selected for various applications is usually dictated by feed and product size distribution. Rod Mills Rod mills are able to accept feeds up to approximately 2", depending on the hardness of the material, and can produce products with maxim um sizes from 4 mesh to as fine as 35 mesh. The rods in a rod mill are in line contact and as a result preferentially grind the largest size particles and produce a product which has a relatively narrow range of size distribution; i.e., very little tramp oversize and very little extreme fines.

Figure 1 shows the various types of rod mill discharge arrangements. Overflow discharge is most common and is used extensively in mining applications. The grinding is done wet and the mill is used to reduce a crushing plant product to a size suitable for ball mill feed .

ROD MILLS Overflow Discharge

End peripheral discharge

End peripheral discharge is used when grinding is to be done wet or dry and a relatively fine product is required. The peripheral discharge is used because it gives a high gradient and good flow rate with dry material. Center peripheral discharge with feed from both ends is commonly used in the aggregate industry for the production of sand. The short grinding length and high gradient result in very rapid discharge and reduced production of extreme fines which are usually undesirable in sand plants . In practice it has been proven that rod mill design is subject to several limitations. The ratio of length to diameter should not be less than 1.2/1. The speed at which the mill is operated should be lim ited to a maximum of 70% of critical speed* and preferably should be in the 60 to 68 percent critical speed range. Ball Mills Ball mills are normally used to produce finely sized products that may range from 35 mesh to 10 microns. In the mining industry the most common flowsheet is made up of crushers, rod mills and then final grinding in ball mills. In the cement industry and in some mining applications, ball mills are used to do primary grinding of a crusher product. As a general rule , hard ores should not be coarser than 80% passing Y4" and soft ores or cement clinker should not be coarser than 80% passing 1" when fed to a ball mill. Larger feed is undesirable because the large ball diameters that become necessary result in high wear and less efficient grinding. Selection of a flowsheet will depend on the characteristics of the feed material and relative capital and operating costs of crushing, rod milling and ball milling. * CRITICAL SPEED: A grinding mill's critical speed is the lowest rpm which will cause an infinitely small particle on the shell liner to centrifuge. This is expressed by the following equation: 76.63 Critical Speed (in rpm) = yO D = Internal diameter of mill in feet, measured inside shell liners

Center peripheral discharge

Example: a mill measuring 11'0" diameter inside of new shell liners operates at 17.3 rpm. Critical speed is 76.63 C.S. = y111= 23.1 rpm Mill speed expressed as a percent of critical speed is 17.3 23.1 = 75% Critical Speed

Figure 1 4

Figure 2 illustrates the various ball mill discharge arrangements. As with rod mills, the most common discharge arrangement on a ball mill is trunnion overflow. This type of mill operates wet, and its major advantages are simplicity of design and easy access for inspection and replacement of liners. Low or intermediate level diaphragm discharge can be applied to either wet or dry grinding. The high gradients that can be obtained with this type of discharge permit rapid flow of dry material, and this helps reduce overgrinding. With diaphragm type discharge, the ball charge can be carried at levels between 45 and 50 percent of mill volume without danger of ball spillage.

BALL MILLS Overflow Discharge

Multiple compartment ball mills are frequently used to produce very high reduction ratios in one unit. The mill is divided into two or more compartments so that the ball charge for each compartment can be sized to achieve the most efficient grinding based on the size of the material entering the compartment. In this way, efficient use of very long mills is possible, and multiple un its, which requ ire extra floor space and auxiliary equipment, are not necessary. Ball mills are extremely flexible in both geometry and the speed at which they can be operated. Mills with lengths between three and five times their diameter are usually selected for applications where surface area of the product is critical and a high recycling load is not desirable. On the other hand, mills with lengths between one and two times their diameter are usually selected for applications where it is desirable to have the product size predominantly in a narrow intermediate range such as is required for liberation of mineral grains from gangue. In this instance , the classifier is expected to remove finished material as soon as possible , and a recyc ling load of 200 to 300 percent of feed rate is desirable. Ball mills have been successfully run at speeds between 60 and 90 percent of critical speed, but most mills operate at speeds between 65 and 75 percent of critical speed.

Pebble Mills Pebble mills are used predominantly for secondary grinding in installations where low media costs and liner wear are of prime consideration and the material being ground is capable of forming suitable pebbles. Pebble mills are similar to diaphragm discharge ball mills in nearly all aspects of design. They are usually run at speeds between 75 and 85 percent of critical speed. Pebble mills are considerably larger than ball mills for the same horsepower input. The power drawn by any mill is proportional to the bulk density of the charge, and because pebbles have a lower bulk density than steel balls, the volume inside a pebble mill shell must be increased proportionally.

Intermediate Level Diaphragm Discharge

Low Level Diaphragm Discharge

Figure 2

5) Dry gri nding uses less media and liner material per ton of material ground than wet grinding .

SELECTION OF WET OR DRY GRINDING Wet grinding is most commonly used in the min ing industry because most subsequent processes such as flotat io n, leach ing or magnetic separation are done wet. In areas where water is scarce or where a dry process follows , grindi ng is done dry. In cement plants , all cl inker grind ing is done dry because of the nature of the material , but both dry and wet processes are used fo r grinding of the raw mix. Some considerations are :

6) Dry grinding , in open circuit, eliminates the need fo r fil tering and drying of product. CHARGE VOLUME The cha rge volume of a ball or rod mill is expressed as the percentage of the volume within the liners filled with balls or rods . When the mil l is stationa ry, the charge volume can be qu ickly obtained by measuring the diameter inside the li ners and the distance from the top of the mil l inside the liners to the top of the charge. The percentage loading or charge volume can then be read off th e grap h in Figure 3 or can be approximated from th e fo llowi ng equ ation:

1) Wet grinding requires less power per to n of material ground than dry gri nding . 2) Wet gri nd ing requires less space than dry grinding if classifiers are requi red. 3) Wet grinding does not require elaborate dust control equipme nt.

%l oadi ng = 113- 126

4) Dry grinding is limited to feed material with a low moisture content. If the moisture co ntent is high, drying is requ ired .

+

where H is distance from top of mill inside of lini ng to top of charg e and D is diameter of mill.

Figure 3

A

c

H

R2 T .---:8

T

,....,_

.4

!'-.. f ' ~"-..

5f--.7

!'-- !"-.

.6

........

.71-:6

.8 .9 1-:5

I'.

........

""'""'

1.6

r-.... 1'--- t--...... ..........

.........

.......... ........

........

1'--..

1.11-:4-

H

1.21---

1--

1.3 1-:3-

T

1.6

1'--- r........ )--..

[".." ['... ['... I""" r-...

..........

1.4

1'---

r........

~

""' "" ' ""' ""

A, Area of

['-.......

Charge

1.3 1.2

!-....... r--...

1.4 f---,1.5 1---

1.5

R

!"'---- r-...

A R,

""' !"'t'-....

~

1.0

I

c ...........

' ~

1.1

1.0 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 % Load

6

Center of Gravity: Read Value on Curve ~ , Mu ltiply by R. Example: loading 38%, R = 7.5 Curve~ reads .527 X 7.5 = 3.95 ft.= C. R Area of Charge: 2 Read Value on Curve ~, Multiply by R • R Example: loading 38%, R = 7.5 Curve : 2 reads 1.2 X 7.52 = 67.4 sq. ft. = A. Top of Charge to Top of Mill: Read Value on Curve ~ , Mu ltiply by R. Example: loading 38%, R = 7.5 Curve ~ reads 1.19 X 7.5 ft. = 8.9 ft. = H.

Maximum power is drawn by a mill when the charge occupies approximately 50% by volume. However, as seen in Figure 4, the power curve becomes very flat in the range above 45%. As a result, mills are seldom run with charge levels greater than 45% . In rod mills, the charge is swollen by particles of feed which separate the rods. If the mill is shut down immediately after the feed is shut off, the charge level will be greater than if the mill had been " ground out" prior to shutdown . Because of this, rod mills are normally operated with a 32 to 40 percent charge by volume. In operation, this becomes a 40 to 50 percent charge, with a bulk density considerably lower than that of stacked rods . Figure 4 00

v /

0

0

60

Max. Power

/

50

I

Draw. 0

"""

I

I

10

0 0

Several other secondary factors enter into the selection of media size : 1) The harder the ore, the larger the media required to break a particle of given size.

3) The faster the mill speed , the smaller the media required to break a particle of given size . The above factors are all taken into consideration in the following equation , which can be used to calculate the maxi mum size media required in a given mill to grind a given material:

-=

fFWi

~\j- KC.

...

rs-

\j Vo

M F

j_

20

2) As the size of the grind ing med ia decreases , the surface area available for grinding small particles increases , resulting in an increased grinding capacity.

M

I

0

1) As the size of the grinding media increases, the pressure between surfaces increases, making it possible to break up larger particles.

2) The larger the mill diameter, the smaller the media required to break a particle of given size.

~

I I/

0

%of

~

L..---

SELECTION OF OPTIMUM SIZE GRINDING MEDIA In any given rod or ball mill , app lication sizing of the media presents a problem because there are two major oppos ing factors:

10

20

30

40

50

60

70

% Charge.

Ball mill charges become measurably swollen only when there is a buildup of large unground material in the ball mill or when the density of the pulp in a wet mill is e~tremely high. Although these conditions are seldom encountered, it is recommended that ball mills be ground out prior to shutdown for measurement of the charge level.

diameter of topsize media in inches size in microns of the screen opening which 80% of the feed will pass Wi work index c. percent of critical speed S specific gravity of feed 0 diameter of mill inside liners in feet K constant, the value of which is 200 for ball mills and 300 for rod mills The above equation gives the maximum size media required for a particular application. This will also usually be the size of media added to the .mill to make up for wear during operation. After a long period of operation , the size distribution of the media will be a complete range from maximum size down to very small size. This distribution of sizes is referred to as a seasoned or equilibrium charge and will be found to be the most efficient charge for nearly all applications.

In order to produce an equilibrium charge as soon as possible after a mill has been started up, the initial charge should be graded with respect to diameter. A list of graded charges for various topsizes is given in Figure 5. Figure 5

approximately 382 lbs./cu . ft. As previously mentioned , the rod charge becomes swollen with ore particles and the bul k density of the total charge can appear to be much lower if proper proced ures are not followed. Broken rods also increase the void space and resu lt in decreased efficiency. Figure 6 is a table of grind ing rod data.

TABLE OF INITIAL CHARGES Rod Diameter (Inches)

5 19 17 16 15 13 10 10

5 4'1. 4 3'1.

3 2'1.

2

4'1.

4

21 19 18 17 15 10

24 23 20 18 15

1 'Ia

Ball Diameter (Inches)

5 4'1. 4

3 2'/a 2 1 'Ia 1 '!.

Figure 6

Rod Size Distribution For Startup Charge (%Weight)

GRINDING ROD DATA

3'1.

3

26 22 20 17 15

30 26 23 21

Ball Size Distribution For Startup Charge (%Weight)

5 17.0 25.0 20.0 15.0 1 0.0 6.4 3.8 2.8

4'/a

4

16.0 30.0 21 .5 14.0 9.1 5.4 2.4 1.6

3

2'/a

2

1'1. 1'/.

1

I

20.0 32.0 21 .0 12.5 8.6 3.4 1.2 1.3

7f. !

3'1.

I

I

I 22.0 I I I 35.0 26.0 I 19.0 36.0 32.0 I I 14.6 22.0 39.0 38.0 I 5.3 9.2 1 6.5 35.0 28.0 2.0 3.2 6.1 13.0 36.0 30.0 1.0 1.7 2.9 6.4 16.0 32.0 22.0 1.1 1.9 1.4 3.1 8.0 14.5 52.0 24.0 2.1 4 .5 12.0 23.5 26.0 76.0 1 00

Rods The rods used as grinding media are hot rolled high carbon or alloy steel . The quality selected should be sufficiently hard to give good wearing properties but not hard enough to cause excessive breakage. The sizes used vary from 5" down to 11/2" diameter. The length of rod used in a given mill will be between 6 and 9 inches shorter than the distance between the head li ners, when new, measured at the shell-to-head junctu re. Charging of rods into the larger mills is done mechanical ly. Charging should be done on a regu lar basis to maintain optimum power demand .

When new rods are placed in the mi ll , they will be in line contact and the void space will be approximately 22% . Thus new stacked rods weigh

8

Rod size (inches) 1Yz 2

2Yz 3 3Y, 4 5

wt./ft. (lbs.) 6.0 10.8 16.8 24.0 32.8 42.8 67.0

Surface area lb./cu. ft. (sq. ft./ton) stacked 131 382 98 382 78 382 65 382 56 382 49 382 I 39 382 I

Balls The balls used as grind ing media are usually of either forged steel or cast Ni-Hard . The choice of ball composition will depend upon the cha racteristics of the material to be ground, the ball size requ ired and the proximity of various suppliers. Preferably, the ball shou ld be as nearly round as possible with no excessive forging or casting ridges. Charging should be done on as frequent a basis as possible to maintain optimum power demand. When new balls are placed in the mil l, they will be in point contact with one another and the void space will be approximately 44%. The we ight of new balls is approximately 280 lb./cu. ft. Figure 7 is a table of grind ing ball data. Figure 7 GRINDING BALL DATA Ball dia. (inches) % 1 1Y.. 1Y, 2 2Y, 3 3Y, 4 5

wt. ea. (lbs.) .063 .148 .290 .501 1.187 2.318 4.006 6.361 ·9.495 18.544

lbs./cu. ft. 280 280 280 280 280 280 280 280 280 280

Surface area (sq. ft./ton) 392.2 294.1 235.3 196.1 147.1 117.6 98.0 84.0 73.5 58.8

When a mill has been operated for a reasonable length of time and the charge has reached an equilibrium condition, the size distribution of the product and recycling loads should be examined to determine whether or not the efficiency can be improved by changing the makeup size of the media.

Pebbles If pebbles are to be used as grinding media, the pebble size used should be such that a rounded pebble will have the same weight as a steel ball that would be required for the same feed and mill conditions. This gives only a first approximation and pebble grinding should be thoroughly pilot tested on any given material. In pebble mills there is no need for a graded initial charge because media consumption is relatively rapid and equilibrium size distribution will be achieved in a relatively short time.

CONSUMPTION OF GRINDING MEDIA Consumption of media in wet grinding results from two major sources. The first is abrasion of the media surface by contact with the material being ground, with the liners and with other med ia. The second is by corrosion of the freshly exposed media surface. Of the two sources, the second appears to make the major contribution to media consumption. Consumption of media in dry grind ing results only from abrasion and is therefore much lower than media consumption in wet grinding. In some cases, coating of the media by material in dry grinding reduces media consumption to very low levels. Figure 8 is a table of expected levels of media consumption.

CALCULATING MOTOR AND MILL SIZE Determining Horsepower Requirement The power required to grind a material from a given feed size to a given product size can be estimated by using the following equation: 10Wi 10Wi

w

where W

= =

-----vP -

\IF

power consumption expressed in kwh/short ton (HPhr/short ton = 1.34 kwh/short ton)

Wi

work index, whic h is a factor relative to the kwh / short ton requ ired to reduce a given material from theoretically infinite size to 80% passing 100 microns

P

size in microns of the screen opening which 80% of the product will pass size in microns of the screen opening which 80% of the feed will pass

F

When the above equation is used, the following points should be borne in mind: a) The values of P and F must be based on materials having a natural partic le size distribution . b) The power consumption per short ton will only be correct for the specified size reduction when grind ing wet in closed circuit . If the method of grinding is changed , power consumption also changes as fo llows: 1) Wet Grinding , Closed Circuit = W 2) Wet Grind ing, Open Circuit, Product Topsize not limited = W 3) Wet Grinding , Open Circuit, Product Topsize limited = W to 1.25W 4) Dry Grind ing, Closed Circu it

Figure 8 MEDIA CONSUMPTION IN LB./TON OF FEED Range

0.1-0.4 Rod Mills Primary Ball Mills 0.1-0.7 Secondary Ball Mills 0.1-0.5

DRY Average

0.2 0.2 0.15

WET Range Average

0.5-2.0 0.5-2.0 0.3-1.5

0.9 0.9 0.8

=

1.30W

5) Dry Grinding, Open Circu it, Product Topsize not lim ited = 1.30W 6) Dry Grind ing, Open Circuit, Product Topsize limited = 1.30W to 2W Open circuit grinding to a given su rface area requ ires no more power than closed c ircuit grinding to the same surface area provided there is no objection to the natural tops ize . If topsize must be limited in open circu it,

power requ irements rise drastically as allowable topsize is reduced and particle size distribution tends toward the finer sizes.

The most reliable work index values are those obtained from long te rm operating data. If this is not avail able standard grindability tests can be run to provide approximate va lues.

c) The work index, Wi , should be obtained from test results or plant data, where the feed and product size distributions are as close as possible to those under study.

Rod and ball mill grindabi lity test results should only be applied to the ir respective methods of grind ing .

The work index, Wi , will vary considerably for materials that appear to be very similar. The work index will also have a considerab le variation across one ore body or deposit.

d) If P is less than 80% passing 70 microns, power consumpt ion will be

w(

P+ 10.3 ) 1.145P

The graph in Figure 9 simpl ifies calcu lation of the power req uirement once the work index is known.

Figure 9 MICRONS 10 100 90 80 70 60 50 40

20

30 40 50

100

500

1000

5000

10,000

30 20

!::

0

....._ I..

...s::::: 0..

:r:

10 9 8 7 6 5 4 3 2

1 .9 .8 .7 .6 .5 .4

,2

.1

I MESH

10

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

I

t

I I I I I I II

-! i i i l " HHH2

Example #1 A wet grinding ball mill in closed circuit is to be fed 100 TPH of a material with a work index of 15 and a size distribution of 80% passing % inch. The required product size distribution is to be 80% passing 100 mesh. In order to determine the power requirement, the steps are as follows: 1) Read the value of work expended in going from infinite size to 80% passing %" on the 15 work index plot. (2.50 HPhr/ton) 2) Read the value of work expended in going from infinite size to 80% passing 100 mesh. (16.5 HPhr/ton) 3) Subtract the work already done on the feed from the total work required to produce the product. (16 .5 -2.5 = 14.0 HPhr /ton) 4) Multiply the feed rate in TPH times the work per ton . (1 00 X 14.0 = 1400 HP)

Matching mill size to horsepower requirement The power requirement calculated above is the power that must be applied at the mill drive in order to grind the tonnage of feed from one size distribution to a finer size distribution . The following shows how the size of mill required to draw this power is calculated : Figure 10 represents a section of a mill in operation. The power input required to maintain this condition is theoretically: hp = (W) (C) (Sin a) (27T) (N) 33 ,000 where W = weight of charge C distance of center of gravity of charge from center of mill in feet a

N

=

dynamic angle of repose of the charge mill speed in rpm

Figure 10

~Nrpm

If data from a similar installation is available , the value of the angle a can be found and the power demand of mills with various diameters at the same speed can be calculated . The value of the angle a varies with the type of discharge , percent of critical speed, and grinding condition . Thus direct comparison can only be made between mills with similar types of discharge. If various types of discharge are to be used , the following factors must be applied for mills of the same size and speed: 1) dry diaphragm = 1.0 2) wet diaphragm = 0.9 3) wet overflow = 0.8 In order to use the preceding equation, it is necessary to have considerable data on existing installations. Therefore , this approach has been simplified as follows: Five basic conditions determine the horsepower drawn by a mill1) Diameter 2) Length 3) % loading 4) Speed 5) Mill type

These conditions have been built into factors which are given in Figure 11 . The approximate horsepower of a mill can be ca lculated from the following equation:

Example #2 In example #1 it was determined that a 1400 HP wet grindi ng ball mill was required to grind 100 TPH of material with a Bond Work Index of 15.0 from 80% passing V4 inch to 80% passing 100 mesh in closed circuit.

HP = A X 8 X C X L where A = factor for diameter inside shell lining 8 = factor which includes effect of % loading and mill type C = factor for speed of mill L = length in feet of grinding chamber measured between head liners at shell-to-head junction

What is the size of an overflow discharge ball mi ll for this application?

· Figure 11 FACTORS FOR CALCULATION OF ROD & BALL MILL HORSEPOWER D iamete r D ia. In side F ac S h ell tor Li ners A

12

8' 8'-6" 9' 9'-6" 10' 10' -6" 11 ' 11 '-6"

32 .0 37 .3 43 .1 49.6 56 .1 63 .5 71 .1 79 .3

12' 12' -6" 13' 13'-6" 14' 14'-6" 15' 15' -6" 16' 16'-6" 17' 17'-6" 18' 18' -6" 19' 19' -6" 20'

88.4 97 .5 108.0 118.5 130.0 141 .5 154.5 167.2 181 .5 196.0 211 .2 226 .7 243 .6 260 .5 278 .9 297.8 317 .1

Mill Type and Load i ng Facto r B Ball Mills

Rod Mills

Dry PeWet % Load - Dry We t Over- riphi ng D iaph . Diaph . flow era I 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

4 .30 4 .57 4 .80 5 .07 5 .31 5.53 5 .71 5 .90 6 .05 6 .16 6 .27 6 .34 6.41 6.46 6.49 6 .50

3 .87 4 .12 4 .32 4.57 4 .77 4 .97 5 .14 5 .32 5.45 5 .55 5 .65 5 .70 5 .77 5 .82 5 .84 5.85

Wet Pe- Wet riph - Overera I flow

3.44 4.73 4.25 3 .66 5.04 4 .54 3 .84 5 .27 4.75 4 .06 5.58 5.02 4 .24 5.82 5 .24 4.42 6 .08 5.47 4 .57 6 .28 5 .65 4 .72 6.48 5 .83 4 .84 6 .67 6 .00 4 .93 6 .78 6 .1( 5 .02 6.90 6 .2 1 5 .08 5 .13 5 .17 5 .19 5 .20 -

Speed

%

% C ritic al Speed

F acto r

c

C ritical Speed

Facto r

60 61 62 63 64 65 66 67 68 69 70 71 72 73

0.1340 .1370 .1400 . 1430 .1460 .1490 .1521 .1552 .1583 .1625 .1657 .1690 .1724 .1760

74 75 76 77 78 79 80 81 82 83 84 85 86 87

. 1798 .1838 .1878 .1918 .1958 .1999 .2040 .2081 .2124 .2166 .2208 .2251 .2294 .2337

c

3 .78 4 .03 4 .22 4.47 4 .66 4 .86 5 .02 5 .19 5 .33 5.42 5 .52

-

Step 1: HP =A X 8 X C X L Step 2: The effective diameter of a mill is the diameter inside lining; i.e., the net diameter. In this case, the mi ll under conside ration is a new installation so liners will be roughly 3" thick and the net diameter will be 6" less than the diameter inside the shell. Since no diameter has been specified, investigate a range to find the most suitable. From the tab le the values of A are: For a net diameter of 10'6" ........ A = 63.5 For a net diameter of 11'6" ...... . . A = 79 .3 For a net diameter of 12'6" ... . .... A = 97.5 For a net diameter of 13'6" . .... .. . A = 118.5 Step 3: Most overflow discharge mills operate with 35 to 45 percent charge. An average value is 40% . The value of 8 from the table for a wet overflow mill at 40% is as follows: 8 = 5.02 Step 4: Speed was not specified , so a range of speeds should be investigated to find the most suitable. From the table the values of C are as follows: For 68% of critical speed ..... . .. C = 0.1583 For 72% of critical speed ..... . .. C = 0.1724 For 76% of critical speed ... . .... C = 0.1878 Step 5: Solving for the length of the mill with 10'6" net diameter, 40% charge and 68% of critical speed required to draw 1400 HP: 1400 L = 63.5 X 5.02 X .1583 = 27 ·7 ft . The length required for each of the above diameters and speeds is tabulated be low . SPEE D NET DIAM ETE R 68% 10'6" 11 '6" 12'6" 13'6"

ocs

27.7ft. 22.2 ft. 18.1 ft. 14.9 ft.

72%

ocs

25.5 ft. 20.4 ft. 16.6 ft. 13.7ft.

76%

ocs

23.4 ft. 18.7 ft. 15.2 ft. 12.5 ft.

Step 6: Choose the particular combination of diameter and length which seems best suited to your application. The following points should be considered in making th is selection: 1) Length to diameter ratio-rod mill ratios normally fall between 1.2/1 to 1.6/1; ball mill ratios normally fall between 1I 1 to 5/1 (see pages 4 and 5). 2) Speed selection-the slower the speed , the less wear on media and liners ; the faster the speed , the lower the capital cost. 3) The mill sizes obtained from the preced ing calculation will be a first approximation only, because just the five major factors that affect horsepower drawn have been considered . Feed size, work index, product size, viscosity, pulp density, ore bulk density, liner design, hydraulic gradient in the mill and quality of media all have an effect on the power drawn and on the efficiency. While the size you select will be accurate enough for preliminary planning, Nordberg should be consulted before the final size selection is made. Nordberg 's engineering staff will determine your requirements with the speed and precision which computer calculations make possible. There is no cost or obligation for this service.

From these figures it is obvious that operating costs overtake capital investment in a matter of a few years. LARGE MILLS vs SMALL MILLS In the design of a large plant there is a choice between the use of many small mills or a lesser number of large mills. Figure 12 shows the percentage variation in cost per installed horsepower of mills and auxiliaries in the range 1000 to 6000 HP. The cost of the building to house a grinding operation of a given installed horsepower has been shown to decrease substantially as the unit size increases and the number of lines decreases. Operating labor costs are conside rably reduced when large units are used. Avai lability of large mills is in general equal to or better than that of small mills. Large mills' availability has frequently been superior because the large units justify mechanization of charging and lining operations. The indication is that the largest possible mills should be considered for each new installation. Figure 12

Cost vs hp relationship I

__\ ' CAPITAL COSTS AND OPERATING COSTS The capital cost of rod, ball or pebble mills will depend on the mill size, the speed and the severity of service. Total installed cost per horsepower, including foundations, services, auxiliaries and building where required, will generally range from two to three times the cost per horsepower of the mill alone. The operating cost per horsepower year of a rod or ball mill, including power, media and liner cost only, will normally range between 50% and 175% of the cost per horsepower of the mill itself, depending on whether grinding is to be wet or dry, the abrasiveness of the feed, and the unit cost of wearing items and power. Cement grinding mills are at the low end of the range and ore grinding mills are at the high end of the range.

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