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Permanent Magnetic Separators
The science of magnetic separation has experienced extraordinary technological advancements over the past decade. As a consequence, new applications and design concepts in magnetic separation have evolved. This has resulted in a wide variety of highly effective and efficient magnetic separator designs.
In the past, a process engineer faced with a magnetic separation project had few alternatives. Magnetic separation was typically limited and only moderately effective. Magnetic separators that utilized permanent ferrite magnets, such as drum-type separators, generated relatively low magnetic field strengths. These separators worked well collecting ferrous material but were ineffective on fine paramagnetic particles. High intensity magnetic separators that were effective in collecting fine paramagnetic particles utilized electromagnetic circuits. These separators were large, heavy, low capacity machines that typically consumed an inordinate amount of power and required frequent maintenance. New developments in permanent magnetic separation technology now provide an efficient alternative for separation of paramagnetic materials.
Technological advances in the field of magnetic separation are the result of several recent developments. First, and perhaps most important, is the ability to precisely model magnetic circuits using sophisticated multi-dimensional finite element analysis (FEA). Although FEA is not a new tool, developments in computing speed over the last decade have made this tool readily accessible to the design engineer. In this technique, a scaled design of the magnetic circuit is created and the magnetic characteristics of the individual components quantified. The FEA model is then executed to determine the magnetic field intensity and gradient. Using this procedure, changes to the magnetic circuit design can be quickly evaluated to determine the optimum separator configuration. This technique can be applied to the design of both permanent and electromagnetic circuits. As a consequence, any type of magnetic separator can be developed (or redesigned) with a high level of confidence and predictability.
Equally important has been the recent development of rare-earth permanent magnets. Advances in rare-earth magnet materials have revolutionized the field of magnetic separation. The advent of rare-earth permanent magnets in the 1980’s provided a magnetic energy product an order of magnitude greater than that of conventional ferrite magnets. Rare-earth magnetic circuits commonly exhibit a magnetic attractive force 20 to 30 times greater than that of conventional ferrite magnets. This development has provided for the design of high-intensity magnetic circuits that operate energy-free and surpass the strength and effectiveness of electromagnets.
Finally, the materials of construction used in the fabrication of magnetic separators have advanced to a point that significantly extends service life while decreasing maintenance. Advanced materials, such as fiber composites, kevlar, ultra high molecular weight polyester, and specialty steel alloys are now commonly used in contact areas of the separator. These materials are lightweight, abrasion resistant, and comparatively inexpensive resulting in significant design advantages as compared to previous construction materials.
The evolution of high strength permanent rare-earth magnets has led to the development of high-intensity separators that operate virtually energy free. The use of rare-earth magnetic separators for beneficiation of industrial minerals has become the industry standard with literally hundreds of separators placed in recent years. The following sections present an overview of the most widely used permanent magnetic separators: rare-earth drum and rare-earth roll-type separators.
Rare-Earth Magnetic Separator Types
There are three distinct types of magnetic separators using rare earth magnets, in addition to simple magnetic traps in the form of rods and grids:
1. Roll separators, see Figure 2, usually with an enveloping belt, supported by an idler roll.
2. Drum separators for dry and wet processing, see Figures 3-6, essentially similar to well-known low-intensity drum separators using ferrite magnets.
3. Matrix-type separators, such as the narrow-width vertical wheel.
Of the roll separators, there are at least fourteen manufacturers. Most of the different makes are based on the original Permroll design concept originated by this author. Various enhancements have been mainly focused on the belt tracking methods. New magnetic roll configurations and optimization of roll designs are relatively recent innovations. Additional optimization efforts are in progress.
At last count, seven manufacturers have commercially available drum separators, most based on magnet circuits derived from the use of conventional ferrite magnet. Two unique designs have been developed with one clearly offering advantages over older configurations.
Rare-earth elements have some unique properties that are used in many common applications, such as TV screens and lighters. In the 1970’s, rare-earths began to be used in a new generation of magnetic materials, that have very unique characteristics. Not only were these stronger in the sense of attraction force between a magnet and mild steel (high induction, B), the coercivity (Hc) is extremely high. This property makes the magnetization of the magnet body composed of a rare-earth element alloy very stable, i.e., it cannot easily be demagnetized.
It was a well known fact that permanent magnets positioned on both sides of a flat steel body can magnetize the steel to a high level, if the magnet poles were the same on each side, i.e., the magnets would repel each other. However, in the past, large magnet volumes were required to achieve any substantial magnetization. With the new powerful magnets, the magnet volume could be relatively small to generate high steel magnetization. In 1981 this author determined the optimum ring size for samarium-cobalt magnets. Maximum steel magnetization (near saturation) could be obtained if the rings were stacked to make a roll using a 4:1 ratio of magnet to steel thickness, see Figure 1. Since magnetized particles are attracted to the magnetized steel surface on the roll periphery, this means that 20% of the exposed roll surface would collect such material. This collection area is an order of magnitude greater than what could be achieved with prior art magnets, making the magnetic roll useful for mineral separation.
Although one of the first prototype rare-earth magnetic rolls was calculated to have about 14,000 gauss steel magnetization, it was found in comparative testing with electromagnetic induced roll (IMR) separators operating at about 21,000 gauss, that similar performance was obtained in fine particle processing (smaller than 1 mm). When processing coarser particles an improved performance was established (e.g., less weakly magnetic contaminants remaining in the upgraded product — and fewer separation passes to achieve high quality). The improvement results because the magnetic force acting on the particles is high, due to a high flux gradient. An electromagnetic induced magnetic roll separator has an air gap, which must be increased to accommodate the processing of larger particles. The rare-earth magnetic roll (REMR) magnetic separator has no such air gap. Consequently, the magnetic force does not decline in the manner of an IMR set with a large air gap.
Magnetic Separators Application in Mineral Industry
One of the oldest tools used in mineral concentrating is the magnetic separator. Virtually every mineral handling system has need for some type of magnetic equipment in two types of basic usage.
- Equipment protection through tramp iron removal.
- Mineral concentration based on.magnetic properties of the minerals contained in the ore.
Magnetic Protection Equipment
Mineral processing plants utilize a variety of material handling systems. The type of magnetic protection applied is normally matched to the system at the point that protection is required.
The types of equipment most commonly protected are:
- Size Reduction Equipment
(crushers, pulverizers, rolls and mills)
- Sizing Equipment
(screens and classifying equipment)
- Material Handling Equipment
(conveyors, bucket elevators, pneumatic systems, etc.)
As the name implies, suspended magnets are installed over conveyors to lift tramp iron out of the burden. Suspended magnets have been more frequently applied as conveyor speeds have increased. Suspended type magnets are capable of developing very deep magnetic fields and magnet suspension heights as high as 36″ are possible.
Suspended magnets are of two basic types – (1) circular and (2) rectangular. Because of cost considerations, the rectangular suspended magnet is nearly always used. Magnet selection requires careful analysis of the individual system to insure adequate tramp iron removal. Factors that must be considered include:
- Conveyor speed
- Conveyor width and loading
- Maximum lump size
- Minimum size of tramp iron to be removed
- Shape of tramp iron to be removed
- Mounting position
The position in which the magnet must be mounted will also influence the size of magnet required. The preferred position is at an angle over the head pulley of the conveyor where the load breaks open and the tramp iron is free to move easily to the magnet face. When the suspended magnet must be mounted back from the head pulley parallel to the conveyor, tramp iron removal is more difficult and a stronger magnet is required.
Magnetic Drum Separators
Magnetic drum separators come in many different styles. Tramp iron drum separators usually use a magnet design referred to as a radial type. In such a unit the magnet poles alternate across the width of the drum and are of the same polarity at any point along the drum’s circumference. The magnet assembly is held stationary by clamp bearings and the drum shell is driven around this magnet assembly.
Drum-separators lend themselves to installation in chutes or at the discharge point of bucket elevators or screen conveyors. The capacity and type of tramp iron to be removed will determine the size selection of a drum separator. They are available in both permanent and electro magnetic types.
Wet Type Magnetic Separators
Wet drum magnetic separators have been applied in several types of service including:
- Media recovery in HMS plants
- Magnetite ore concentration
- Removal of grinding iron from ball and rod mill pulps.
- Recovery of precipitated cobalt and nickel
Standard drum diameters are 30″ and 36″. General guide lines, in diameter selection, are based on (1) feed volume (2) magnetic loadings and (3) particle size. The 30″ diameter drum guide lines are roughly maximum of 75 GPM per foot feed volume, 8 TPH per foot magnetic loading and 10 mesh particle size. The 36″ guide lines are 125 GPM per foot feed volume, 15 TPH per foot magnetic loading and 3/8 inch particle size.
For many years, wet magnetic drum separator magnet rating has been on the basis of a specified gauss reading at 2″ from the drum face. The gauss reading is an average of readings taken at the centerline of each pole and the center of the magnet gap measured 2 inches from the drum surface. This rating tends to ignore edge of pole readings and readings inside of the 2 inch distance, particularly surface readings which are highly important in effective magnetic performance.
Dry Type Magnetic Separators Alternating Polarity Drum Separators
We have previously discussed dry drum separators as used for tramp iron removal. A second variety of drum separator is the alternating polarity drum separator. This separator is designed to handle feeds having a high percentage of magnetics and to obtain a clean, high grade, magnetic concentrate product. The magnet assembly is made up of a series of poles that are uniform in polarity around the drum circumference. The magnet arc conventionally covers 210 degrees. The magnet assembly is held in fixed operating position by means of clamp bearings and the cylinder is driven around this assembly.
Two styles of magnet assemblies are made up in alternating polarity design. The old Ball-Norton type design has from 8 to 10 poles in the 210° arc and develops a relatively deep magnetic field. This design can effectively handle material as coarse as 1 inch while at the same time imparting enough agitation in traversing the magnetic arc to effectively reject non-magnetic material and produce a clean magnetic concentrate product. The 30″ diameter alternating polarity drum is usually run in the 25 to 35 RPM speed range.
Application of the high intensity cross-belt is limited to material finer than 1/8 inch size with a minimum amount of minus 200 mesh material. The cost of this separator is relatively high per unit of capacity approaching $1000 per inch of feed width as compared to $200 per inch of feed width on the induced roll separator.
Alternating Current Matrix-Type Magnetic Separator
This investigation for an improved separator is a continuation of the previously reported pioneering research of the Bureau of Mines on the matrix-type magnetic separator. When operated with direct current. or a constant magnetic field, the matrix-type magnetic separator has several disadvantages, which include incomplete separation of magnetic and nonmagnetic components in one pass and the retention of some of the. magnetic fraction at the discharge quadrant. Since the particle agitation that results from pulsed magnetic fields may overcome these factors, operation with an alternating current would be an improvement. Another possibility is the separation of dry feeds, which may have applications where the use of water must be avoided.
The effects of an alternating field were first described by Mordey and later by others of whom Doan provides a bibliographical resume. The significant feature to note in the description by Mordey is the change from a repulsion in weak fields to an attraction in strong fields, in addition to a difference in response with different minerals. The application by Mordey was with wet feeds using launders and inclined surfaces, although applications by others are with both wet and dry feeds.
Except for occasional later references the interest in alternating current for magnetic separation has almost disappeared. Lack of interest is probably due to the apparent high power consumption required to generate sufficiently intense magnetic fields, a problem that warrants further consideration.
Equipment and Procedures
The matrix separator differed somewhat from the slotted pole type described in a previous report in that the flux passed into the matrix from only one side, the inverted U-shaped magnet cores 4 and 7 illustrated in figure 1. Figure 1 shows a front view, side view, and a bottom view of the matrix-type magnetic separator. By this arrangement, an upward thrust could be exerted on the matrix disk during each current peak; the resulting induced vibration would accelerate the passage of the feed as well as the separation of the magnetic particles from the nonmagnetic particles since the applied field during the upward thrust preferentially lifts
the magnetic particle. Besides the preferential lift, the alternating polarity produces a vibration of the magnetic particle as a result of the magnetization delay or hysteresis.
The matrix disk 5 rotates successively through field and field-free quadrants. Where a given point on the disk emerges into a field quadrant, feed is added from a vibrating feeder; nonmagnetic particles fall through the matrix, and magnetic particles are retained and finally discharged in the succeeding field-free quadrant.
Two types of disks were used, a sphere matrix illustrated in top and cross-sectional views in figure 2 and a grooved plate type similarly illustrated in figure 3. Both the spheres and grooved plates were mounted on a nonmagnetic support 1 of optimum thickness for vibration movement (figs. 2-3). The sphere matrix disk, similar to that of the earlier model, had a matrix diameter 8 of 8.5 inches and spokes 7 spaced 45° apart; the spheres were retained by brass screens 4 (fig. 2).
The grooved plate disk was an assemblage of grooved steel plates that tapered so that one edge 5 was thinner than the other 6 (fig. 4) to provide a stack in the form of a circle having an outside diameter 9 of 7.9 inches (fig. 3). The plates were retained by two split aluminum rings 8 and 3 clamped in two places 1 and 11. They were stacked so that the vertically oriented grooves of one plate touched the flat side of the second plate. As illustrated in figure 4, two slots 3 and 4 were added to reduce eddy current losses.
Both disks 5 illustrated in figure 1 were rotated by a pulley 1 through a steel shaft 8 held by two aluminum bars 2 and which in turn were fastened to aluminum bars 3 and steel bars 6. The magnetic cores 4 and 7 were machined from 10- by 12-inch E-shaped Orthosil transformer laminations. For wet feeds,
the addition of feed and wash water was the same as described in a previous report. With dry feeds) the feed was added close to the magnet pole from which the rotating disk emerged.
With the information derived from the performance of this separator, a cross-belt-type separator was also constructed as illustrated in figure 5, which shows a front view and a cross-sectional view through the center of the magnet core. The cross-belt separator mentioned here differs somewhat from the conventional cross-belt separator in that the belt 5 moves parallel to the feed direction instead of 90° with the feed direction. The magnetic core, composed of parts 17, 19, 21 and 22 that were machined from 7-½-by 9 inch E-shaped Orthosil transformer laminations, supplies a magnetic field between one magnetic pole 6, which has grooves running parallel to the feed direction, and the other magnetic pole 14. Owing to the higher intensity field at the projection from the grooves, magnetic particles are lifted from feeder 15 to the belt 5. By movement on flat-faced pulleys 3 supported by bearings 4 the belt 5 carries the particles to the discharge chute 7. Nonmagnetic particles fall from the feeder edge and are discharged on the chute 8. A special 0.035-inch-thick Macarco neoprene-dacron endless belt permits a close approach of the feeder surface to the magnet pole 6. The feeder 15 constructed of plexiglass to prevent vibration dampening by eddy currents, is fastened to a vibration drive at 16 derived from a small vibrating feeder used for granular materials. A constant distance between poles 6 and 14 was maintained by acrylic plastic plates 9 on each side of the poles 6 and 14 with a recessed portion 13 to provide room for the belt 5 and feeder 15. The structural support for the separator, which consisted of parts 1, 2, 11, 18, and 20, was constructed of 2- by 2- by ¼-inch aluminum angle to form a rectangular frame, and part 10 was machined from angular stock to form a support for the magnet core.
Each U-shaped magnet core in figure 1 was supplied with two 266-turn coils and two 133-turn coils of No. 10 AWG (American wire gage) heavy polythermaleze-insulated copper wire. With alternating current excitation, the current and voltage are out of phase so that the kilovolt-ampere value is very high even though the actual kilowatt power is low. This difference may be corrected with either series capacitors to reduce the input voltage or parallel capacitors to reduce the input current. However, the circuit that was selected is illustrated in figure 6 in which the two 266-turn coils are connected in series with the capacitor 2. Power is supplied by the 133-turn drive coil 7 that is connected in series with the 133-turn drive coil 9 on the other U-shaped magnet core. Coils 4 and 6 and the capacitor 2 form a circuit that resonates at 60 hertz when the capacitor 2 has a value of 49 microfarads in accordance with the equation
f = l/2π (LC)-½…………………………………………………………….(1)
where L is the inductance of the coils in henries, C the capacitance of the capacitor in farads, and f is the frequency in hertz. At resonance the inductive impedance XL,
XL = 2πfL……………………………………………………..(2)
equals the capacitive impedance Xc,
Xc = (2πfC)-¹…………………………………………………….(3)
For the capacitance in the power input circuit, the value is calculated on the basis of the equality of equations 2-3. When the input at point 10 is 10 amperes at 126 volts or 1.26 kilovolt-amperes, the current at point 3 and the voltage at
point 1 are 10 amperes and 550 volts, respectively, or a total of 11.0 kilovoIt-amperes for the two magnet cores, which provides a 5,320-ampere- turn magnetization current. The capacitors, a standard power factor correction type, had a maximum rating of 600 volts at 60 hertz.
Application of alternating current to the cross-belt separator is not successful. In contrast to the matrix-type separator in which the feed is deposited on the magnetized matrix, the feed for the cross belt is some distance below a magnet pole where the field is weaker and the force is a repulsion. Even though the magnetic force with the matrix-type separator may be a repulsion instead of an attraction, it would result in the retention of the magnetic fraction in the matrix. Replacement of the alternating current with an intermittent current eliminates the repulsion effect but still retains the particle vibration characteristics.
For an intermittent current the circuit shown in figure 7 is used. A diode 5 supplies the current to a coil 4, which can be the magnetizing coil for the cross-belt separator, or for one magnet core of the matrix-type separator that is connected in parallel or series with the coil for the other core. A coil 2 is supplied with half-wave-rectified current from a diode 6 but is out of phase with the other coil 4 and is only applicable to a second separator. However, the circuit illustrates the reduction of the kilovolt-ampere load of intermittent magnetizing currents. As an example, measurements were, made with the two magnet cores of figure 1; each core had 532 turns of wire. When the capacitor 9 has a value of 72 microfarads, the current at point 8 is 13 amperes, and the voltages at points 10, 1, and 7 are 75, 440, and 390 volts, respectively. The kilovoIt-ampere input at point 11 is therefore 0.98, and the kilovolt-amperes supplied to the coils is 5.07. This circuit is not a simple resonance circuit, as shown in figure 6, but a circuit in which the correct value of the capacitor 9 depends on the current. At currents lower than 13 amperes, the 72-microfarad value is too large.
However, separations with intermittent current were confined to a simple one-diode circuit. With the matrix-type separator, each magnet core carried 10.5 amperes at 240 volts through 399 wire turns or a total of 21 amperes since the two cores were connected in parallel. For the cross-
belt separator illustrated in figure 5, five 72-turn coils and one 96-turn coil wound with No. 6 AWG heavy polythermaleze-insulated square copper wire were used in series connection. Current-carrying capacity is approximately 40 amperes with an input of approximately 80 volts of half-wave-rectified 60-hertz current. At 40 amperes, the average number of ampere turns would be 18,240. Intermittent current and voltage were measured with the same dynamometer meters used for alternating current; these meters measure an average value.
It is possible to increase the magnetizing current for the matrix-type separator without excessive vibration by increasing the thickness of the plate 1 (figs. 2-3). Another alternative is a combination of intermittent and constant magnetic fields. Although a variety of circuits are possible, the combination of fields was accomplished with the simple adaptation of the stray field losses in a U-shaped magnet core using the circuit of figure 8. The power drawn is full-wave rectification, or half wave for each leg of the magnet core with the flux, from the coils 3 and 4 adding. Owing to magnetic leakage, the flux from the coil nearest to the magnet pole tested predominates. When the magnetic field is measured with a Bell model 300 gaussmeter and observed with a Tektronix type 547 oscilloscope with a type 1A1 amplifier, the results of figure 9 represent a pulsating magnetic field on top of a constant magnetic field plateau.
Separation of Wet Feeds
Although it is known that minerals in water suspension may be separated in the constant-field matrix-type separator at fine sizes, some tests were conducted to investigate if any beneficial effects exist with an intermittent field. One advantage that was found with a minus 325-mesh feed was an increase in the completeness of the discharge of the magnetic fraction with an intermittent field as illustrated in tables 1-2. Both tests had the same average current of 10.5 amperes through the magnetizing coils of each magnet core illustrated in figure 7. The matrix consisted of 1/16-inch-diameter steel spheres.
In the two short-period comparative tests, the wash water for removing the magnetic fraction was the same and was of a quantity that permitted complete discharge with the intermittent field and partial removal with the constant field. After the test was completed, magnetic particles retained with the constant field were determined by a large increase in the intensity of flow of wash water, a flow volume that would not be practical for normal operation. For separation efficiency, the intermittent field had no advantage over the constant field probably because of a lack of vibration response with minus 325-mesh particles at 60 hertz. This will be described later with dry feeds.
Separation of Dry Feeds
Dry magnetic separation at coarse sizes is not a problem because it may be accomplished with a variety of separator types. Difficulty at fine sizes is twofold. First, the feed rate capacity decreases in the separators with moving conveyor surfaces such as the induced roll and cross-belt separators in which the attracted magnetic particles would have to move at nominal feed rates through a thick layer of nonmagnetic particles; second, an agglomeration effect is present that increases with decrease in particle size.
Results of the separation of several mineral combinations in the size range of minus 200 plus 325 mesh are summarized in tables 3-5. Table 3 illustrates the separation of α-Fe2O3 from quartz in an ore with one pass through a matrix of 1/8-inch-diameter steel spheres using the alternating current circuit of figure 6.
The results are equal to that which can be obtained in wet separations. One advantage of dry separations is that the added expense of thickeners and other solid-liquid separation devices is avoided.
Application of an intermittent field with a matrix of 75 percent 1/16-inch-diameter steel spheres and 25 percent 1/8-inch-diameter steel spheres is illustrated in table 4 in a one-pass separation of pyrrhotite from quartz using the circuit of figure 7. Unlike table 3, no attempt was made to obtain an intermediate fraction, which would have resulted in raising and lowering the iron compositions of the magnetic and nonmagnetic fractions, respectively, and provided a fraction for repass with increased recovery.
Table 5 gives the results of the application of a partially modulated field using the circuit of figure 8 and the grooved plate matrix of figure 3 in a one-pass separation of ilmenite from quartz. The advantage of the grooved plate over the spheres is that the particles pass through the matrix in a shorter time. The high flow rate obtained using the grooved plate could be increased further, particularly if water is used, by attaching suction chambers under the disk in a manner similar to applications with continuous vacuum filters. Although the grade and recovery of ilmenite are very high, this need not necessarily be attributed to the grooved-plate matrix since the ampere turns are higher than in any of the other tests. Increased ampere turns is a prerequisite for successful application of alternating current separators and intermittent current separators.
Dry Separation at Finer Sizes
When a minus 325-mesh fraction is tested, a separation sometimes occurs, but in most cases the feed passes through without separation. Response at higher frequencies was investigated with a smaller ¾-inch-cross section U-shaped magnet core 1 (fig. 10). Separation was performed with a nonmagnetic nonconducting plane surface 3 moved manually across the magnet pole as illustrated by the direction arrow 4. When separation occurred, the nonmagnetic mineral 5 would move with the plane, and the magnetic mineral would separate from the nonmagnetic mineral by remaining attached to the magnet pole. When no separation occurred, the entire mixture of magnetic and nonmagnetic minerals would either move with the plane or adhere to the magnet pole.
Four magnetising coils of 119 turns each of No. 14 AWG copper wire were used; three were connected in series with a capacitor as in figure 6, and one was connected to a variable-frequency power supply. The current in the resonant circuit is approximately 5 amperes. When the capacitor has a value of 49 microfarads, the resonant frequency is 130 hertz, and no separation occurs. With the capacitor reduced to 10 microfarads to provide a resonant frequency of 300 hertz, a separation occurs. In the case of a minus 325-mesh α-Fe2O3-quartz mixture, most of the quartz moves with the plane, and the α-Fe2O3 remains attached to the magnet pole. Similar results are obtained with pyrrhotite-quartz. Indications are that the separation may be improved with preliminary treatment of the feed by dry grinding aids.
The relation of frequency and particle diameter is evidently the result of the magnetization delay factor. With very high
frequencies, the time per cycle is too short to permit initial magnetization; at very low frequencies, the magnetization is in phase with the field. The frequencies reported here are between these two extremes and probably near, and just above, the low frequency limit. Experimental values on particles in the size range of minus 35 plus 65 mesh were previously published. These data indicate that 0.16 second, the time required to traverse a magnetizing field distance of 0.9 inch at 5.5 inches per second, is adequate time for the magnetization of minerals, but 0.02 second, the time required to traverse approximately 0.1 inch at the same rate, is too short. Time lag has been reported in the literature for magnetic alloys and has been classified, to the exclusion of the eddy current lag, into a lag that is dependent on impurities and a Jordan lag that is independent of temperature.
From evidence derived from the Barkhausen effect, the magnetization does not proceed uniformly and simultaneously throughout a specimen but is initiated in a limited region from which it spreads in a direction parallel to the field direction at a finite velocity. In a changing magnetic field, the number of initiating nuclei is proportional to the cross-sectional area perpendicular to the direction of the field. For a specimen in the form of a cube, the rate of energy W transferred to the cube would therefore be proportional to the aforementioned cross-sectional area so that for a cube of side s,
dW/dt = a s²…………………………………………………………….(4)
and the total energy in the cube would be
W = bs³………………………………………………………..(5)
where a and b are constants and t is the time. Combining equations 4-5 and integrating, the frequency f is then
f = 1/t = – 1/s a/b ln W……………………………………………(6)
This relation is in accordance with the experimental results in which the frequency increases with decrease in particle diameter although the first-power relation has not been verified.
Application of intermittent current to the cross-belt separator arose from the need for the dry separation of an iron composition material from the copper in a product submitted by personnel of a Bureau of Mines chalcopyrite vacuum decomposition project. Although this product was of a relatively coarse size, the matted mass resulting from the needle shape or fiber form of the copper and the magnetic field coagulation effects of the magnetic particles prevented use of commercial dry separators such as the induced roll separator and constant-field cross-belt separator. The pulsating magnetic field had a separation effect similar to the pulsations in a hydraulic jig; the pulsating magnetic field permits the nonmagnetic fibers to sink back to the vibrating feeder and allows the magnetic particles to rise to the belt. Other applications would include fibrous minerals such as tremolite, actinolite, and chrysolite, and matted and fibrous secondary materials.
Application of alternating and intermittent current to magnetic separation at a relatively high number of ampere turns was made possible by special electronic circuits. Actual power losses are low and include the I²R loss, which is the same that occurs in direct-current magnetic separation, and the core loss, which has a magnitude corresponding to the I²R loss. Minerals may be dry-separated close to the minus 325-mesh size at 60-hertz frequency and possibly at smaller particle sizes at higher frequency. In the wet separation of minus 325-mesh feeds, intermittent current provides for complete release of the magnetic fraction during the discharge cycle. For matted fibrous and magnetically coagulating feeds, a cross-belt separator with an intermittent magnetizing current provides efficient separations.