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About the Media Charge_Lin ear Wear_Ball MillsSpreadsheet
...
Scope :
The Media Charge_Linear Wear_Ball Millsspreadsheet was designed
to estimate the Linear Wear Rate Constantsfora ball charge in a
Conventional Ball Mill, as a function of its known dimensions and
basic operating conditions. Also, thespreadsheet allows for the
calculation of the typical Grinding Media Consumption
Rateindicators; that is, gr/ton,gr/kWh, kg/hror tons/month.
Theoretical Framework :
The most widely accepted mathematical description of the gradual
consumption process experienced by a grinding ball
inside a tumbling mill is known as the Linear Wear Theory, by
which the mass rate of consumption of a grinding ball isdescribed
as directly proportional to the surface area exposed by such ball
to the various wear mechanisms (abrasionand/or corrosion) active in
the mill charge environment :
t = d(mb)/d(t) = - kmAb
where :
Wt = mass wear rate, kg/hr
mb = ball weight, kg; after t hours of being charged into the
mill.Ab = exposed ball area, m2
km = mass wear rate constant, kg/hr/m2.
Equivalently, taking into account the geometry of the grinding
body (sphere or cylinder), one obtains :
d(d)/d(t) = - 2 km/ rb = - kd
where :
d = size (diameter) of the grinding ball, mm; after t hours of
being charged into the mill.
rb = grinding ball density, ton/m3
kd = wear rate constant, mm/hr.
If kdis to remain unaffected by the extent of wear; that is, k
dis not a function of the current ball size d - a
conditionsatisfied by most grinding media varieties and normally
referred to as Linear Wear Kinetics- the above expression mayb i l
i t t d t bt i
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be simpl integrated to obtain
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Moly-Cop Tools TM
Remarks
Power, kW
Mill Dimensions and Operating Conditions 3,348 Balls
Diameter Length Mill Speed Charge Balls Interstitial Lift 0
Overfilling
ft ft % Critical Filling,% Filling,% Slurry Filling,% Angle, ()
536 Slurry
18.50 22.00 72.00 38.00 38.00 100.00 35.00 3,885 Net Total
rpm 12.82 10.00 % Losses% Utilization hr/month 4,316 Gross
Total
% Solids in the Mill 72.00 97.00 698 3,014 MWh/month
Ore Density, ton/m3 2.80
Slurry Density, ton/m3 1.86 Charge Apparent
Balls Density, ton/m3 7.75 Volume, Ball Density
m3 Charge Interstitial above Balls ton/m3
Ore Feedrate, ton/hr 400.0 63.76 296.48 47.48 0.00 5.395
ton/day 9,312
Energy, kWh/ton (ore) 10.79
Make-up Ball Size, mm 75.0 gr/ton gr/kWh (gross) gr/kWh (balls)
Kg/hr tons/monthScrap Size, mm 12.0 625.4 57.96 74.72 250.2 175
Spec. Area, m2/m3(app) 63.78 Wear Rate Constants,
Total Charge Area, m2 4067 mm/[kWh(balls)/ton(balls)] 1.400
mm/hr 0.0158
Purge Time, hrs 3,985
DETERMINATION OF WEAR RATE CONSTANTS
Ball Recharge Rate
Base Case Example
Special Case : BALL MILLS
Mill Charge Weight, tons
Slurry
Moly-Cop Tools/ 251351243.xls.ms_office 11/16/2014 / 10:32
AM
