shaker screen performance
Particles in dry bulk materials are noted in a variety of shapes, sizes, surfaces, densities, and moisture content. Each condition must be taken into consideration when attempting to predict screen performance, through its effect on capacity in terms of weight passing a given screen opening per unit area. The combined effects on screen performance, or “screen ability”, of particle shape, surface texture, and surface or internal moisture, are beyond the reach of empirical solutions based only on size and density, independent of these variables. More exact information on their influence needs to be gained from actual laboratory testing.
SIZE AND SHAPE
The shape of an individual granule may be angular, spherical, acicular, ovaloid, flaky, or slabby. They can be combined with the same material, as sawdust in wood flakes. Separation cutpoint sizes in most screening applications range downward from 4” to 325 meshes (.0018”). The cutpoint defines the smallest particle size retained on the screen, and the maximum undersize particle passing. Unless the particle is acicular, platy, ovaloid or a perfect sphere, it will be probably (but not necessarily) be sized by its largest dimension5.
For any given shape and size distribution, bulk density in lb./cu. ft. (PCF) for any material will be precisely proportional to its specific gravity. Screening is essentially a volumetric measurement, but capacity, or the rate of passage through the screen, is typically charged in units of weight per unit time, based on a standard bulk density of 100 PCF. The actual rate for a material of different bulk density has to be adjusted by the ratio PCF:100. Tables of bulk density for various materials can be discovered in most material handling publications6.
Moisture in granular particles may be absorbed, adsorbed, or both. Either condition can impair screen ability, but tolerance is much greater for internally absorbed than for exterior surface moisture. Surface moisture causes particles to stick together, resisting stratification. Allowable surface moisture for the unimpaired tedious screening of inorganic granular or pelletized particles ranges from bone dry for screen openings below 20 mesh, to 3% for 1/4” openings. Absorbed moisture in permeable soils such as ground clay can block the screen openings with cumulative buildups of extreme fines attached to the screen wires. Absorbent grains such as corn, soybeans, wheat etc. will screen freely after drying to 13-15% internal moisture. Screening of wood chips, flakes and sawdust are unimpaired up to about 30% of internal moisture; however, in laboratory tests with sawdust, efficiency was reduced by almost 60% when moisture was increased to 68%.
The size distribution of particles in a bulk granular material is the primary characteristic that governs the rate of undersized passage through a screen opening that is larger than the smallest particle and smaller than the largest particle in a representative sample of the material. Size distribution is measured by sieve analysis, using a series of standardized wire mesh sieves with square openings that progress, in the commonly used Tyler standard scale7, at the fixed rate of √2 from 1.05” to.0029” (200 mesh). The size distribution is given in the weight percent of each fraction between successive sieves in a series. If the weight is plotted on the y-axis against the mean size of each fraction of the x -axis, the result will resemble a frequency distribution curve.
A more useful graphic form is the logarithmic probability grid, utilizing a two or three-cycle log scale as the ordinate and the probability scale as the abscissa. Tyler Standard Screen openings are spaced equally on the log scale (y-axis), and the cumulative weight percent retained (or passing) on the probability scale (x-axis). The expansion of the probability scales outward from the mean emphasizes the extremes of the particle size distribution. Prints of this grid, shown in Fig. 1, can be consulted on the Internet. Fig, 2 is a sieve analysis of a sample of community limestone plotted on this grid, using the ordinate for the sieve opening and the probability axis for cumulative weight percent passing or retained on each sieve in the series. A different distribution, for a sample of natural sand from a “face” sand deposit, is shown in Fig. 3. These two sieve analyses can be utilized to illustrate the influence on screen performance of differences in particle size distribution.
A “cutpoint”, at the intersection of a line drew horizontally from the y-axis, and a vertical line from the x-axis, defines the percent of the feed that passed the selected opening in the test sieve used for the sieve analysis. This is the reference for calculating the efficiency of any other screen having the exact same opening. The test procedure is designed to allow all the particles that can pass the opening sufficient time to get through, recognizing that, as the effective particle diameter approaches the screen opening dimension, the chances for it to get through the opening diminish as the square of the difference between them. The rate of change of this difference is expressed by the slope of the distribution curve as it passes through the cutpoint. In practical applications, as the rate increases (the slope becomes steeper) the decreasing proportion of particles approaching the opening dimension has two benefits: (1) the cutpoint becomes sharper, with consequent improvement in separation efficiency; and (2) it may allow for an increased opening dimension, improving yield in the fraction under the desired cutpoint, without exceeding specified oversize limits.
As an example, refer to Fig. 2, the sieve analysis of a sample of community limestone. The curve slopes steeply between about 8 mesh and 48 mesh. If the desired cutpoint is within that range, at 28 mesh, and the screen opening is increased one full interval on the Tyler scale, to 20 mesh, the undersize fraction in the feed will increase from 64 to 67%, from the addition of the 3% 20x28 m. fraction.
While the probabilities of the passage of all particles 28m and smaller are improved by the larger opening, thus increasing the undersize yield, the probability that a 28m. The particle will be found in the undersize has only been increased from zero to 1 chance in 30.
Compare this with the flatter distribution of Fig. 3. If the desired cutpoint is set at 28 mesh, at 84% passing, and the screen opening is enlarged one interval to 20 mesh, the undersize fraction in the feed will increase by 8%, to 92%. The probability for passage of the 28 mesh particle into the undersize is the same as in the previous example, meaning that the potential for exceeding a specified limit for oversize in the undersize fraction is almost 3 times greater for the flatter distribution.
As a general rule, screen capacity at any given level of efficiency, other things being equal, will be a function not only of the size of the aperture, but also on the slope of the size distribution curve through the cutpoint. This latter characteristic is taken into consideration in the test-data-based Fractional Efficiency calculations8. The Capacity Estimating Methods9, at a baseline efficiency of 85%, include correction factors for variances in the slope of a known or assumed size distribution.
The Screening Media
There are many varieties of screening media. The most common, available in carbon steel, stainless or other metal alloys, is woven wire screen, made with openings that may be either square or rectangular. Others include profile bars, perforated plates, polyurethane and rubber. The importance of making the best selection of media for any screening application cannot be overstated. In any screening machine, the media will affect performance in terms of capacity, efficiency and cost. Manufacturers of screening equipment will offer their recommendations. Much has been written on the subject10, but often the best results are achieved through trial and error.
Screening requires relative motion between the sieve and the particle mass. In a few specialized cases the sieve is stationary, but in most commercial screening applications, the particle mass flows over a sieve to which some kind of motion is mechanically applied. Its velocity determines the volumetric flow rate of the particle mass over the sieve, whose motion is designed to enhance both the flow and the passage of undersize through the sieve. This motion takes several different forms, being dependent on the design of the screening machine. It may be circular in the horizontal plane; gyratory, with a vertical rocking oscillation superimposed on the circular motion; oscillating in a straight-line, simple harmonic motion; vibrating with a circular motion in the vertical plane; vibrating with a linear pitching motion on a horizontal sieve having both vertical and horizontal components; or vibrating only in the vertical direction. In each case, the surface is sloped as required to obtain the desired mass flow, usually at velocities between 40 and 100 fpm.
In most designs the screen media, if woven wire, is stretched taut over a supporting frame and the vibration is applied through the frame. The vibration is forced, usually by rotating unbalanced weight(s) powered by an electric motor. For circular motion in the horizontal plane, the unbalance is rotated on a vertical axis. Circular motion in the perpendicular plane is generated by unbalances rotating on a horizontal axis. Straight-line motion is produced by one or more of a pair of unbalances contra- rotating on horizontal axes. The unbalances are driven by an electric motor(s), usually through V-belt transmissions, or in a few designs directly connected to, or mounted on, the motor shaft.
These forced-vibration systems are self-balancing, in that the forcing mechanism is an integral part of the vibrating frame so that the Wr of the mechanism equals the Wr of the vibrating assembly, which is plastically supported on springs.
The tuned spring-mass, or natural-frequency, vibrating conveyor is sometimes adapted, in balanced or unbalanced versions, to screen applications.
In a few exceptions, the vibration is applied directly to the screen media mounted in a stationary frame. The vibrating force can be generated by rotating unbalances, or by electromagnetic vibrators.
Mechanical details and performance claims for each type are described, more or less accurately, in the manufacturers’ literature.
MOTION IN THE HORIZONTAL PLANE (SHAKING SCREENS)
In most of the designs employing motion, in the horizontal plane, the amplitude and frequency (rpm) are fixed. Amplitudes range from 1/2” up to 1-1/2” in the oscillating, (straight-line), and up to 3” mean diameter in the circular and elliptical designs. Straight-line oscillating motion is produced by one or more pairs of unbalance weights contra-rotating on a horizontal axis. Circular motions are produced by weights rotating on a vertical axis. This axis may be slightly inclined to produce a gyratory effect. Frequency, or rpm, is selected for peak accelerations of up to 3-1/2 g.12. The axis of rotation may oscillate slightly to produce a gyratory motion. In all but the gyratory designs, the screen surface is sloped slightly to induce or enhance material flow. At a slope of 5°, the force component normal to the surface is a small fraction, about 1/4 to 1/3, of the weight of the particle mass on the surface.
This is the distinguishing characteristic of all the horizontal motion designs: the particle mass slides smoothly over the screen without bouncing, providing for the stratified undersize particles the best opportunity to search for and pass an opening. The advantage is somewhat diminished by the ease with which an on-size particle can be locked in an opening, resulting in progressive blinding of the screen. For that reason, these machines must all incorporate some means for impacting the screen surface from underneath to dislodge the stuck particles. The most common is the resilient elastomeric (bouncing) ball, supported under the screen by a coarse wire mesh, and contained in groups of three or more within a matrix of confined areas. The random impacts of the balls against the screen prevent the emergence of progressive blinding. As an additional benefit, the transient local turbulence caused by the impacts improves efficiency by roughing up the smoothly flowing material bed to prevent packing.
Vibrating screens are characterized by motion components in the vertical plane ranging from +/- 3.5 to 6g or more. The lifting and dropping effect expands the material bed; individual particles are bounced along over the screen with reduced opportunity for finding and passing an opening. This is a disadvantage, compared with the smoother horizontal motion designs. But on the plus side, the strong normal force component acts to eject near-size particles stuck in the openings. Thus resisting progressive blinding, and the turbulent expansion of the material bed prevents packing. These advantages gain strength with increasing bed depth and particle size.
The two most common types of vibrating screen are the inclined and horizontal. In the inclined screen, the single unbalance, rotating on a horizontal axis, generates a circular motion in the vertical plane. Since this motion has no positive transport property, the screen surface is sloped at 15-20° to cause the particle mass to travel at velocities of 60 – 100 fpm. The horizontal screen employs a pair of unbalances, rotating in opposite directions on parallel horizontal axes, to generate a straight-line reciprocating motion, inclined to the plane of the screen surface at 40 – 50°. Travel rates on a horizontal surface range between 60 and 80 fpm , and can be increased if necessary by inclining the screen downward at up to about 10°.
The vibrating conveyor is in the same class as the horizontal vibrating screen, but with significant differences that limit its usefulness for screening. Its natural frequency operating system, intended for conveying dry bulk granular materials on a smooth surface, is fixed in a longer stroke, lower frequency regime than the vibrating screen. Peak accelerations are generally below the threshold for blinding prevention. Efficiency, mediocre at best, deteriorates rapidly for separations below about 1/8”.
Vibrating screen performance can be optimized for any application by changing amplitude (stroke) and frequency (cpm or rpm). Tests have shown that the screening rate is more responsive to changes in amplitude than in frequency13 (Fig. 4), although higher frequencies are helpful in resisting nearsize blinding. As a general rule, the amplitude should increase with particle size, or increased bed depth, and frequency adjusted to maintain peak acceleration in the normal range of +/- 4-6g14. Amplitude and frequency are related to peak acceleration in simple harmonic motion, or centripetal acceleration in circular motion, in the simplified formula
g is a multiple of the normal acceleration due to gravity;
N= frequency (rpm or cpm)
S= total stroke (in.)
The relationship between feed rate (proportional to depth of material bed) and optimum amplitude at constant rpm is illustrated in Fig. 5. Note that in this test peak efficiency was obtained at successively greater amplitudes as feed rate was increased, but the relative efficiency at each successive peak declined, as shown by the optimum amplitude envelope line. This was only one test sequence, on a laboratory-sized inclined circle-throw vibrating screen, but it supports a cautious generalization that there is no one combination of frequency (rpm or cpm) and amplitude that can promise best performance without confirmation by test, in any particular application and feed rate.
In the special case where vibration is applied directly to a woven wire screen cloth, creating a unidirectional vibration normal to the screen surface, the amplitude is limited by the strength of the screen wires, but the frequency is variable, up to about 3600 cpm. The limited amplitude is compensated for with a steep inclination of the screen surface, in the range of 35 - 45°. The screening action is created by the vibration of the screen cloth, which slightly stretches the wires and discourages plugging with nearsize particles. Obviously, applications are limited to fine screening, with wire diameters less than about .025”. The width of screen openings needs to be increased to correct for the slope, by dividing the desired cutpoint by the cosine of the angle.
Fig 1. Log probability graph corrdinate
Fig 2. limestone size distribution
Fig3 Frac sand sample FSI
Fig 4. Relative screening rate vs Amplitude frequency
Fig 5. OptiMum amplitude envelope