(1974) oswald, d. j.ziegler, j. g._inventory control of grinding mills using bearing pressure...

8/17/2019 (1974) Oswald, D. J.ziegler, J. G._Inventory Control of Grinding Mills Using Bearing Pressure Measurement

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Inventory Control of Grinding Mills Using

Bearing Pressure Measurement

by D.

1

Oswald and

1

G. Ziegler

lt is of common knowledge that loading within a grinding mill, whether ball, rod,

pebble, or autogenous, is direct ly related t o the lubrication back pressure developed

between th e mill journal and bearing shoe during mill operation. The merit s of both

forced-feed and gravitational-feed bearing lubrica tion methods are discussed wit h

particular emphasis directed toward their applicability to continuous grinding mill

inventory control. Data obtained from wet grinding mill applications in t he cement

and mining industries is presented to more clearly define the influence of such var i-

ables as feed consistency, slurry viscosity, mill re tention, bearing oil temperature,

grind fineness, and grinding media wear o n the measured journal lubrication back

pressure during automatic mil l feed control. Finally, various grinding mill control

schemes for maintaining constant mill loading and consequent l~ optimizing mill

operating efficiency are discussed and evaluated as to their advantages and/or dis-

advantages.

Th e primary concern in the design of an y grinding

process is to achieve and maintain the most efficient

grinding mill operation with minimal expense of grind-

ing time and media wear. People, knowledgeable of

grinding processes and their characteristics, generally

agree that optimum mill performance is dependent on

an accurate control of both slurry consistency and ore-

to-media ratio inside th e mill.

Slurry consistency is adequately controlled either b y

measuring slurry density and regulating the addition of

mill water, or b y ratioing the primary water directly to

the weight o f primary feed.

Various methods of mill inventory control have been

proposed, including measurement o f recirculating load,

mill

power draw, slurry density , media sound, and

various combinations. However , th e success of these con-

trol schemes has been marginal, due to their inherent

inability to consistently and accurately detect variations

i n mill loading.

Th is paper discusses th e basis of efficient grinding mill

operation and describes a mill inventory control method,

which was investigated b y the authors and demonstrated

unusually high sensitivity to variations in mill inven-

tory. This method, known as the Harris Bearing Pres-

sure Method; infe rs mill loading by measuring the

hydrodynamic oil pressure developed between the mill

trunnion and bearing during normal mill operation.

The feasibility of implementing bearing pressure

measurement to mill inventory control is evaluated, and

a grinding control loop, capable of maintaining a con-

stant mill slurry consistency and ore-to-media ratio, is

proposed.

brief explanation of the theory of bearing pressure

measurement is included, and expressions relating pres-

sure sensitivity and magnitude to known mill parame-

ters is empirically derived.

D.

J

OSWALD is Systems Engineer and

J

G. ZIEGLER is Senior

Systems Engineer, Taylor Instrument Process Control Div., Sybron

Corp., Rochester, N. Y. TP 718130, A lM E Centennial Annual Me et-

ing, New York, March 1971. Manuscript, Mar. 9, 1971. Discussion of

this paper, submitted in duplicate prior to Sep. 15, 1973, will appear

in SME Transactions, December 1973, and in AlME Transactions,

1973, Vol.

254.

Efficient M ill Operation

T o obtain the most efficient grinding mill operation an

accurate control of both slurry consistency and ore-to-

media ratio is required. The te rm slurry consistency

refers to the ratio of solids to liquids i n the mill slurry,

while ore-to-media ratio defines the degree o f mill load-

ing.

It is desirable in most grinding processes to coat the

surface of the grinding media-whether balls, rods, or

pebbles-with a th in layer of slurry. Thus, as the media

cascades and cataracts with normal mill rotation, the

layer of slurry adhering to th e media is subjected to

continuous grinding. This action facilitates the size re-

duction of mill slurry and accelerates the grinding

process.

I f the slurry consistency i n a mill is too low, as ofte n

exists i n the grinding of harder ores, the resulting media

coating is minimal and excessive media-to-media con-

tact exists. This condition is undesirable and costly for it

increases th e rate o f media wear.

Too high a slurry consistency, as experienced in soft

ore grinding, inhibits the natural tumbl ing motion o f the

media, due t o the high viscosity of t he slurry. This re-

duces mill grinding efficiency.

The slurry consistency at which most grinding mills

operate is approximately 65 solids.

te rm that indicates the degree o f mill loading is th e

ore-to-media ratio. Some grinding industries re fe r to

this ratio as the M/V ratio, where M represents the total

volume of slurry in the mill and V represents the vol-

ume of interstitial voids between the grinding media (V

equals approximately 38 of a bulk ball charge).

s

an

example, a M/V ratio of defines a mill loading in which

the slurry exactly fills the voids between the media.

Typical M/V ratios range fro m to 5, while bulk grind-

ing media charges normally vary from 20

to

50 of

mill volume.

Th e efficiency of grind is affected b y the ratio of ore-

to-media loading inside a mill. I f the ratio is too small

(insuffi cient sl ur ry) , media grinds against other media,

th us causing premature media and liner wear. Too large

a ratio (excess ive slurry) cushions the media impact and

restricts th e grinding motion o f the media. condition

of op timu m mill loading exists wh en most o f the media

TRANSACTIONS OL. 254

Society of Mini ng Engineers, AlM E SEPTEMBER

1973 01


2/5

t X = Optimum MI V Ratio

Fig. 1-Mill grind ing

efficiency vs. ore/ball

g

ratio. Mill Underload Mill Overload

ORE/

BALL

RATIO

r

M IV RATIO

grinds most of the slurry most of t he time The specific

inventory level which satisfies this condition is not read-

ily defined for all grinding processes, but must be de ter-

mined for each individual case through a trial and error

approach.

M il l Inventory Control Loop

The primary concern in most grinding mill applica-

tions is to establish an operating slurry inventory and to

maintain this inventory regardless of any variations in

feed grindability and/or recirculating load. The deter-

mination of the optimum inventory is dependent on the

ore-to-media or M/V ratio th at allows the mill to oper-

ate at its peak efficiency. As illustrated in Fig. 1 and dis-

cussed previously, it is undesirable from a standpoint of

mill grinding efficiency to either underload or overload

a mill with slurry.

The inventory of a grinding mill consists of basically

four components:

1)

raw feed, (2) recirculating feed

(oversize grind),

3 )

water, and

(4)

grinding media.

Of

these, the variation i n recirculating feed causes the most

difficulty with present inventory control techniques.

The percentage of recirculating feed is directly af-

fected by changes in the grindability of the raw feed

and the grinding efficiency inside the mill.

Generally

speaking, the quantity of oversize grind from th e classi-

fier increases with an increase in feed size and/or

hardness.

Fig.

2

shows a closed loop grinding process that uses

the Harris bearing pressure principle to maintain mill

inventory. In t he event of a change in mill loading oc-

curs, due to a change in feed grindability and/or recir-

culating load, pressure controller PC-1 senses a change

in mill bearing pressure and commands weight control-

ler WC-1 to provide more or less primary feed to the

mill, in order to restore optimum ore-to-media loading.

Primary water to the mill is ratioed directly to the

weight of pr imary mill feed by ratio relay FY-1. This is

done to prevent wide variations in mill slurry consist-

ency, which, as mentioned previously, affects mill

grinding efficiency.

The mill output is collected in a slurry sump, whose

level is maintained by water addition, controlled by

level controller LC-1. The slurry i s pumped from the

sump to the classifier, where the acceptable product of

specified fineness is separated from the oversize grind.

The fines continue on for additional processing, while

the oversize r etu rn to the mill for fu rther grinding.

The advantage of the Harris method, as compared to

existing inventory control methods, is that bearing pres-

sure measurement provides a t rue indication of total

mill loading. Consequently, it can directly compensate

for variations in feed grindability without requiring a

separa te measurement of recirculating load.

M il l Slurry Density Control

If slurry consistency is not adequately controlled by

ratioing primary water to mill feed, it may be necessary

to control the density of slurry to th e classifier by trim-

ming the flow of pr imary water. The output of the

density controller would provide a bias signal to the ra-

tio relay FY-1 that would raise or lower the set point of

flow controller FC-1 to maintain a proper primary water

flow for the desired slurry density.

To ensure a tru e measurement of mill slurry density,

it

is

advisable to control output sump level by recircu-

lating slu rry to the sum p rather th an by w ater addition,

as shown in Fig. 2. This level control alt ernative is only

applicable to closed loop systems whose classification

methods do not require a constant flow of slurry.

Med ia Wear Control

Maintaining an optimum mill ore-to-media ratio re-

quires not only a knowledge of variations in slu rry in-

ventory, but also a n awareness of any decrease in total

media volume due to inherent grinding wear. Increased

media wear must be compensated with reduced slurry

loading, i f mill gr inding efficiency is to be maintained.

Bearing pressure measurement is not capable of dif-

ferentiating between a decrease in mill loading due to

slurry inventory change and that due to inherent media

wear. Consequently, as media wear increases, bearing

pressure control compensates for the subsequent loss in

mill loading by increasing the mill throughput. This re-

sults in an increase of th e ore-to-media ratio (M/V ra-

tio), a decrease in mill grinding efficiency, and a tend-

ency toward mill overloading (ref er to Fig. 1).

Compensation for loss in mill loading due to media

wear i s feasible by periodically reducing the mill inven-

tory setting on controller PC-1 in Fig. 2, consistent

with the ra te of media wear. This action prevents a mill

Fig. 2-Bearing

grindin g process.

pressure control of a

typical

Primary Water

1

202

EPTEMBER

1973

Society of Min ing Engineers Al ME

TRANSACTIONS OL. 254


3/5

overload condition from occurring and maintains a near

optimum ore-to-media ratio inside the mill.

Investigations conducted on mill power draw vs. mill

inventory levels show that mill power draw is more

sensitive to changes in mill media volume than to

variations in mill throughput.' Assuming th is to be true,

it may be possible to remotely set the inventory setting

of PC-1 with a measurement of mill power draw. The

feasibility of this has not been investigated, but is the

next logical step toward total automatic inventory con-

trol.

Bearing Pressure and Its Mea surem ent

Having described a typical pressure control loop, the

question to be answered is, Is the sensitivity of this

method adequate to measure and control variations in

mill inventory? The remaining sections consider the

principle of bearing pressure measurement and derive

expressions tha t are capable of approxim ating the pres-

sure sensitivity and range for any grinding mill appli-

cation.

A rigorous mathematical analysis describing the dy-

namic operation of a journal bearing may be found in

any machine design handbook. This paper discusses only

the basic principles.

Fig. 3 shows a typical oil lubrication system character-

istic of many grinding mills. As the mill rotates, lubri-

cant from the gravity reservoir flows onto the trunnion

and is subsequently squeezed between the bearing and

rotating trunnion. The formation of this lubricating

wedge develops a fluid pressure film between the rotat-

ing members, capable of exerting sufficient pressure to

separate the two surfaces and to support the trunnion

load. The excess lubricant, squeezed from between the

trunnion and bearing, is collected in an oil reservoir

and is transported via a low pressure pump,

back to

the gravity feed reservoir for recirculation.

The hand pump and high pressure lubricating line in

Fig. 3 is used for mill start-up purposes only. Before

starting a mill it is necessary to unseat the trunnion

from the bearing to avoid frictional damage to the soft

babbitted bearing. Lubricant is squeezed between the

two stationary members until the trunnion floats. The

pressure measured during start-up is considerably

higher than that measured during normal mill operation.

The maximum lubricating pressure developed is usu-

ally located near th e base of th e bearing. The pressure

decreases nonuniformly along the width and length of

the bearing, reducing to

0 psig at the bearing periphery.

As the trunnion load increases, inferring an increase

in mill inventory, the lubricant between the trunnion

GRAVITY FEED

RESERVOIR

b Lubricant

Table

1.

omenclature

b

Bearing pressure magnitude, psig.

Bearing pressure sensitivity inventory change ), psi per lb.

A,rr Effective bearing area, sq. in.

f e Effective bearing ratio.

D

Bearing diameter,

in.

L

Bearing width, in.

Bearing contact angle, degrees.

6 integration limit on bearing angular length, degrees.

Coordinate along bearing width.

Coordinate along bearing angular length.

and bearing is forced to flow through a smaller diame-

ter opening, thus increasing the lubricating fluid pres-

sure. Likewise, bearing pressure decreases when a re-

duction in mill inventory occurs. It is this correlation

between mill inventory and bearing pressure that forms

th e basis for th e Harris Pressure Control Technique.

Refer to Fig. 3. Pressure Transmitter PT-1 measures

the pressure in the start-up line, which during normal

mill operation equals the lubrication pressure b

(see

Nomenclature, Table 1) a t the base of the bearing.

Pressure Controller PC-1 adjusts the mill feed in rela-

tion to the bearing pressure variation detected by PT-1.

Reducing valve PCV-1 is included in the system to

protect transmitter PT-1 against the high lubrication

pressures developed during mill start-up.

The measurement of bearing pressure may be made

at any location along the in ternal bearing circumference.

However, as the point of measurement progresses fur-

ther away from th e base of t he bearing, reduced pres-

sure magnitudes are to be anticipated.

The babbitted bearing in Fig. 3 is shown with a trun-

nion contact angle of 180 ; typical mill bearing contact

angles range from 90 to 180 .

Bearing Pressure Magnitude and Effective Area

A relationship is derived in the Appendix that en-

ables one to estimate th e bearing pressure b for any oil

lubricated mill. The results show that bearing pressure

is directly related to the trunnion load and is inversely

proportional to the effective bearing area,

Ae r

which

supports th is load.

For convenience, A e r r s expressed as a percentage of

the projected bearing area, L. This percentage is

referred to as the effective bearing ratio f and is a func-

tion of the bearing contact angle

a

as shown in Fig. 4.

For example, the effective area of a 180 bearing is 32%

of the projected area,

x

L; th e effective ar ea of a 120

bearing is 24% of the projected area.

Although the bearing relationship derived assumed a

uniform bearing pressure profile (see Appendix), the

High Pressure Lubrication

.BABBITTED

.

ESERVOIR

LOW

PRESSURE

PUMP

o

o

M i eed

Controller WC-l

Reducing Valve

I

or Transmitter Protection

during Mi l l Startup

Fig. 3-Bearing pressure meas uremen t and in-

strumentation.

T R A N S A C T I O N S O L . 2 5 4

Socie t y of M i n i ng Engi neers , A l M E

SEPTEMB ER 1973 03


4/5

bearing pressures recorded from the mills investigated,

and those calculated from the derived equations agreed

closely. For example, one mill investigated had a 120

bearing, 54 in. diam

x

26 in. width. The trunnion load

was estimated at 288,000 lb. Referring to Fig. 4 and

substituting into Eqs. 7 and

9

in the Appendix resulted

in a bearing pressure estimate of 860 psig. The bearing

pressure recorded during field testing was approximately

875 psig. Similar calculations on other mills substan-

tiated the validity of th e relationship derived in the

Appendix.

Bearing Pressure Sensitivity

The resultant change in bearing oil pressure with a

change in mill inventory is termed the bearing pressure

sensitivity S. An expression relating this pressure sensi-

tivity to known mill parameters is derived by differen-

tiating Eq. 7 with respect to trunnion load and equating

this to a change in mill inventory.

Bearing pressure sensitivity, as stated in Eq. 11, has

units of psi per pound inventory change and is inversely

proportional to the effective bearing area A.rr, defined

by Eq. 9.

Consider a mill with a slurry inventory of 15 tons and

a pressure sensitivity of 4 psi per ton. If this inventory

increases by 10% or 1.5 tons, a bearing pressure increase

of 6 psi occurs. This pressure change is adequately mea-

sured by a force balance transmit ter of 50 or 100 psi

span. More readability is achieved by decreasing the

span of the pressure transmitter.

It is apparent from Eq. 11 that maximum sensitivity

is obtained when the effective bearing area is a mini-

mum. Referring to Eq. 9 and Fig. 4, minimization of

effective bearing area is accomplished by reducing the

physical dimensions of the bearing; namely, width, di-

ameter and contact angle. The limiting value on these

parameters is usually determined by mill speed, size,

and loading. Consequently, nothing can be done on ex-

isting mills to improve bearing pressure sensitivity. On

new mill designs, it is desirable to minimize the size of

the bearing, consistent with loading requirements, to

achieve the maximum pressure sensitivity.

The pressure sensitivity for the mills investigated was

approximately 3 psi per ton inventory change. The cal-

Load. Ibr.

I

Fig. Effective bearing

ratio vs. contact angle.

PC Oil Pressure , p s i

0

90

IXT

160.

1 8 0

CONTACT ANGLE a

culated and recorded magnitude of pressure sensitivity

agreed within 10%.

Summary and Conclusions

The applicability of the Harris Bearing Pressure

Method to grinding mill control was investigated for

several grinding mills including ball, semi-autogenous,

and combination rod-ball mills. The results of this in-

vestigation showed that the lubrication pressure devel-

oped between the trunnion and bearing varies directly

with mill inventory.

It was concluded that bearing pressure control can

adequately maintain mill inventory independent of vari-

ations in feed grindability and/or recirculating load.

This method is only applicable to grate discharge mills

where inventory level changes with feed rate. Bearing

pressure control is not an acceptable control for open or

overflow discharge mills.

Grinding processes that use bearing pressure control

require periodic up-dating of the desired mill inventory

level to compensate for inherent wear of the grinding

media. The frequency of adjustment is dependent on

the rate of media wear and varies with the grinding

application.

A reasonable approximation of bearing pressure sensi-

tivity and magnitude Pa is obtained from the following

equations (see Appendix) :

Trunnion Load

PI = (psig) (7)

Aetr

where

Aerr

= x

(D

x L

(sq in.)

(9)

D, L, and f , denote the mill bearing diameter, width, and

effective bearing ratio, respectively.

Insufficient time was available during this investiga-

tion to determine the ore-to-media ratio tha t resul ts in

the most efficient mill performance. Additional time and

testing is necessary to provide an answer to this ques-

tion. The investigation concluded that bearing pressure

measurement is applicable to mill inventory control.

However, the effects of media wear, oil temperature,

lubrication feed, etc., must be evaluated to gain

a

clearer

indication of its performance. Fur ther investigation is

in process.

Appendix

The following exercise develops an expression for

bearing pressure magnitude P O s a function of known

mill parameters. (See Table 1 for Nomenclature.)

Refer to Figs. 4 and 5. It i s assumed that the bearing

pressure measurement is made at the center of the

bearing

e

=

0,

Z

=

0). For proper mill operation, the

trunnion load must be balanced by the total sum of

forces developed in the lubricant.

Consequently,

Trunnion Load = ZF, = ~ ~ d F c o s 8 .

1)

The force at any point along the bearing surface may be

expressed as

d F = P x dA

D

where P P (e, z)

;

dA e dz.

2

Substituting,

.

D

Trunnion Load P (0, z) cos

0

do dz (3)

204

EPTEMBER

1973

Society of Mining

Engineers, AlME

TRANSACTIONS OL.

254


5/5

Rotolion

Trunnron Trunn ion Load

f n

atural

Lubrimtion

Pressure

Film /

\

Tunnm

Fig.ynamics.Bearing pressure

I f i t is assumed tha t bearing pressure is max im um at

2 ~ ~ , ' ' ~

m nx 1

- )

( 1

- )

cos

e

d e d r .

( 5 )

Integrating Eq. 5,

T ru nn io n Load P,.,

2 eo

1 6 )

Solving Eq. 6 fo r P,., yields ,

Trunn ion Load

Pa Pm,,

Aerr

(7)

where A.,, is the ef f ect ive bearing area i n vert ical sup-

port of th e trunnion load.

( 1 o s eo

A ,,

X

2

eo

I f the quant i ty D x n Eq. 8 is defined as the bearing

projected area,

A.1,

may be represented as a ratio f o f

this projected area.

z

0 ,

0,

and zero at

z

e,, and i f laminar ( 1

-

os a /2 )

2'

f a

( 1 0 )

f low is assumed (un i fo rm pressure decay along th e bear-

ing sur face ) , h e fo llowing equat ion may be wri t ten:

where 200. Calculated values o f f . are given i n Fig. 4.

P ( ~ , z )P

(

- I ) 1 - l G l ) * 4 )

References

1

U.S. atent No. 3,350,018.

Per ry, J.H.. Perry s Chemical Engineers Handbook, McGraw-H ill.

Substituting Eq. 4 into Eq. and considering th e bearing

New Yo rk . 1963.

3 Taggert. A.F. Handbook of Mineral Dressing, John Wil ey, New

and pressure symmetry, Yo rk , 1960.

haracterization and Extraction of Metals from Sea Floor

Manganese Nodules

by D. W. Fuerstenau,

A.

P. Herring, and

M.

Hoover

T h e dissolution of nick el, copper, and cobalt from five d iffe ren t samp les of wel l-

characterized deep sea manganese nodules was measured as a function of tempera-

ture , pH, leaching ti me , and particle size. Nic kel, copper, and cobalt ex traction each

respond to these variables in a dif lerent manner. T he results o f this investigation

indicate that copper and nickel can be selectively dissolved from iron and manganese

at moderately low pH, provided the reaction is given suficient t ime .

A

high dissolu-

t ion of cobalt w ith dilute sulfuric acid can only be achieved f ro m nodules that have a

low iron content (

(1974) oswald, d. j.ziegler, j. g._inventory control of grinding mills using bearing pressure...

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