Closed-Circuit Reduction-Stage Capacities

Thus far we have considered open circuit crushing through the several reductions in a multi-stage plant. Very rarely are we able to turn out a finished product without closing the flow-line circuit somewhere along the line. Without going into any argument for or against closed-circuit crushing in any of the various stages, let us examine just what effect closing the circuit will have upon the required capacity for any particular stage.

Consider, for example, a single gyratory crusher of any type, arranged to operate in closed circuit with a vibrating screen, and set so that 70 percent of the original feed will be crushed to a size that will pass through the screen openings. Also, for the sake of simplicity, let us assume that the screen will take out all of this 70 percent undersize, will perform at 100 percent efficiency.

Then, for each 100 tons of original feed to the crusher, 70 tons will pass on as finished product, so far as the stage we are considering is concerned and 30 tons will return to the crusher, on the first pass.

Now, we have to make another assumption, which probably is not strictly in accord with actuality, but seems to be close enough to the mark to suit all practical purposes: we assume that the material returned to the crusher in the first, or any succeeding, pass will be processed in exactly the same fashion as the original feed, i.e., crushed to the same percentages of undersize and oversize. On the basis of this assumption, we would crush 70 percent of the 30-ton fraction to finished size, returning 30 percent, or 9 tons, to the crusher. At the next pass we obtain from this 9-ton fraction, 6.3 tons undersize, and 2.7 tons oversize. The process can be worked out by simple arithmetic to a fairly close approximation by calculating three or four passes; but it will be evident to the mathematically-minded that a simple convergent geometrical series is involved, which can be expressed by the formula:

(1)     T = 100 ( 1 - R )

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