The aim of our research paper was to apply Box-Behnken experimental design and response surface methodology for modeling of grinding beach sand ore using ball mill. The Box-Behnken experimental design was used to provide data for modeling and the variables of model are time of milling, speed of the mill, ball size, number of balls, density of material, feed size and feed quantity. Maximum specific surface is obtained at higher speed of the mill (85 RPM in our case). This also correspondence to the speed at which we have minimum energy consumption per unit surface area generated. Specific surface area created increases with increased in cylinder size. The increase is rapid for larger cylinder sizes. Specific energy consumption is almost same for all cylinder sizes. Specific surface area decreases with increase in feed quantity. Energy required for the unit surface generated has a minimum value at 400 g of feed. Specific energy consumption also decreases with feed quantity at all ball sizes. The specific surface area generated increases with additive quantity for a cylinder size of 0.875 inches and above. Energy savings, expressed as a percentage of the energy consumption without additive, increase with an increase in the additive quantity. The increase is rapid between 1.25 and 2.5 % of feed quantity. Using these sets of experimental data obtained by mathematical software package (MATLAB 7.0), mathematical models were then developed to show the effect of each parameter and their interactions on product. Predicted values and obtained values using model equations were in good agreement with the experimental values. This study proved that Box-Behnken design and response surface methodology could efficiently be applied for modeling of grinding of beach sand ore using ball mill.

The Study yielded the following Equation:

RANGE OF BALL MILL DESIGN FACTORS STUDIED ARE

Variables Minimum Maximum Max/ Min Time of milling, min 5 60 12 Speed of the mill 24 85 3.53 Ball size 1/2 1 2 Number of 1„cƒnballs 10 150 15 Number of 3/4„cƒnballs 50 237 4.74 Number of 1/2„cƒnballs 50 800 16 Feed size, ƒÝ 231 1731 7.5 Feed quantity, gm 200 1500 7.5

NOMENCLATURE

Bs = diameter of the ball, m Dm = average diameter of the particle, m Fs = average diameter of the feed, m g = acceleration due to gravity, m/s2 N = number of revolutions per minute, rpm Ps = average product diameter, m Q = feed quantity, kg S = surface area of the product, m2/kg t = time of milling, s V = linear velocity of the mill at the outer surface, m/s Ws = mass of the balls, kg Y1 = correlation factor

Keywords: Box-Behnken design; Response surface methodology; Modeling, Ball mill