Technical Notes - Fundamentals of Statistical Screening

Statistical screening is so named because a particulate feed is separated into "size" intervals on the basis of the probabalistic behavior of the individual particles (i.e., their probability of passing the screen) rather than by physical restraint. To illustrate this statement, consider a conventional screening operation. A particle which is larger than the openings in the screen cloth is physically restrained from passing through and is repeatedly reflected from the surface until it is discharged as oversize. Of those particles smaller than the screen openings, the very smallest tend to pass the screen near the feed end while those nearer in size to the screen opening tend to pass at a greater distance from the feed end. Alternatively, we could say that the particles with high probability of passing through the screen are concentrated near the feed end while particles of low probability of passing are dispersed from the feed end. This tendency to segregate is the basis for size separation by statistical screening. The purpose of this note is to: 1) Show that the distribution of material passing an array of screens can be described by a modified binomial distribution. 2) Demonstrate that an efficient size separation can be made by this technique. 3) Relate some of the more important screening parameters to the efficiency of the size separation. The Distribution Function The distribution of undersize products along the length of a screen can be derived with the help of a few simple definitions and assumptions. 1) First, we must assume that each particle has some probability of passing a screen on a single presentation. Further, we must assume that this probability is constant and is not affected by the position of the particle on the screen. It must also be acknowledged that several factors enter into this probability. Among them are the "action" of the screen, the slope of the deck, the shape of the openings, etc. The relationship between these factors, however. is not the subject of this paper. 2) To simplify calculations, all particles falling within a size range on the Tyler scale, e.g., —x + x/ mm, are assumed to have the same probability. 3) It is assumed that particles which do not pass the screen on a presentation are reflected a unit distance forward, i.e., the direction of material travel. A unit distance is defined as the distance between the centers of consecutive wires in the screen cloth.