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Separation of small nonferrous particles using an angular rotary drum eddy-current separator with permanent magnets
Int. J. Miner. Process. 78 (2005) 22 – 30 www.elsevier.com/locate/ijminpro
Separation of small nonferrous particles using an angular rotary drum eddy-current separator with permanent magnets Mihai Lungu * Department of Physics, West University Timisoara, Blv. V. Parvan No. 4, Timisoara 1900, Romania Received 30 December 2004; received in revised form 16 July 2005; accepted 18 July 2005 Available online 24 August 2005
Abstract The paper presents a method for separating the small metallic nonferrous particles from two component nonferrous mixtures using a new type of dynamic eddy-current separator with permanent magnets. The so called Angular Drum Eddy-Current Separator (ADECS) consists of a horizontal rotary drum covered with permanent magnets, alternately N–S and S–N oriented. The rotor is placed oblique, under the superior part of a horizontal conveyor belt, coplanar with its surface. The axis of the drum and the direction of displacement of the belt make a certain angle, depending on the physical properties of the particles subjected to the separation process. The separator functions on the basis of the jump effect of the strongly conducting particles which assume different trajectories in the active zone of the field, namely, upper part of the drum. The experimental results and comments regarding the values obtained for grade and recovery for wastes consisting in Cu–Pb and Cu–Al mixtures are given. D 2005 Elsevier B.V. All rights reserved. Keywords: Eddy-current separator; Grade; Nonferrous; Poorly conducting particles; Strongly conducting particles; Recovery
1. Introduction Eddy-current separation methods are used both for recovery and purification of conductive nonferrous metals (Cu, Al, Pb) and also for separating various nonferrous metals from each other (Rem, 1999; Schloemann, 1975). In eddy-current separators, the eddy currents are induced in the nonferrous metallic particles due to the
* Tel.: +40 256494068; fax: +40 256490333. E-mail address: [email protected]. 0301-7516/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.minpro.2005.07.003
changing magnetic field in the active zone of the separator. The interaction between these currents and the magnetic field results into repulsive electrodynamic forces on the metallic particles and so into their separation from nonconductive ones, or from each other (Rem et al., 1996; Schlett and Lungu, 1999). The time dependent change of the magnetic field can be obtained by different devices. Eddy-current dynamic separators with permanent magnets represent a class of separators substantially improved in the last few years, where the magnetic field is generated by machinery with moving permanent magnets. By using permanent magnets, strong fields can be generated,
M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30
therefore the operation costs of eddy-current separation are considerably reduced and the construction of the equipment can be less complex. The eddy-current separators have been developed for the recovery of nonferrous metals from mixtures of waste materials, i.e. shredded car scrap, granulated power cables and municipal solid wastes (Schloemann, 1975; Van der Valk et al., 1986). Although eddy-current separation is used for a wide range of particles sizes and materials, different rotor designs are actually used, the specific choice depending on the feed characteristics and the separation. Machines designed for small particles have many magnet poles of small width, while machines for large particles have a few large poles. These machineries have the same problem, namely a high cost because of the length of the permanent magnets. Yet, the main problems associated with eddy-current separation are those referring to the selective separation of conductive nonferrous particles smaller than 5 mm from nonconductive ones or one from each other, while reducing the cost of the separation process. These particles are difficult to recover with conventional eddy-current separators of the rotary drum type, and are even harder to separate these fractions into the various alloys. The reason is that, for such particles eddy-current separation force (i.e. the tangential force which will be described in the theoretical part) produces acceleration less than the acceleration gravity. As a consequence, the frictional forces which appear due to movement of the particles and acting in the direction opposite to the tangential force will tend to dominate. This paper describes a new type of eddy-current separator with permanent magnets, namely, the angular-drum eddy-current separator (ADECS), designed for separation with a higher efficiency the mixtures of conductive nonferrous and nonconductive particles, or strongly conducting and poorly conducting nonferrous particles, smaller than 5 mm. The separator consists of a horizontal spinning drum, covered with rows of permanent magnets, alternately N–S and S–N oriented, placed oblique under the superior part of a horizontal conveyor belt, coplanar with its surface, as in Fig. 1. The axis of the drum makes an angle a with the direction of the belt. This angle depends on the physical properties of the particles subjected to the separation process, i.e., the elec-
23
Fig. 1. A basic diagram of the separator.
tric conductivity, shape, dimensions and their proportions in the waste. A similar separator is the horizontal drum eddycurrent separator (HDECS) which uses a conveyor belt to feed the material over a rotor with permanent magnets, mounted concentrically within the pulley of the belt. The length of the magnets is equal with the active width of the belt, and the feeding of the particles is made on the whole breadth of the belt. Unlike HDECS, in the case of the ADECS the feeding of the particles (from constructive reasons) is made only on the half of the belt width and, consequently, the magnets are long just about half than the belt width. So, the first reason to use an angular drum is the lower cost of the separation equipment than the conventional HDECS. The feed material is introduced into the active zone of the field by the conveyor belt over the rotary angular drum, and the functioning of the separator is based on the jump effect of the strongly conducting particles. This effect, responsible for the separation of the particles in the case of ADECS and undesired in the functioning of the conventional HDECS, will be described in the theoretical part of the present paper. Under the combined actions of electromagnetic interactions, gravitational and frictional forces, the particles of the feed material describe various trajectories on the surface of the belt, depending on their physical properties. Thus, the poorly conducting and strongly conducting particles or conductive nonferrous and nonconductive particles obtain different trajectories and leave the end part of the belt on different ways, leading finally to their separation. The drum and the belt are coplanar and made the angle a in the horizontal plane that is the incident
24
M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30
angle for the feeding particles, in order to obtain a maximum efficiency of the separation process. The repelled particles are represented by the strongly conducting particles in the case of mixtures containing strongly conducting–poorly conducting particles and conductive non-ferrous particles in the case of mixtures containing conductive non-ferrous–nonconductive particles, respectively.
2. Theoretical considerations Eddy currents are induced in a conductive nonferrous particle placed in the active zone of the separator as a response to the magnetic field, which changes rapidly in time due to the rotation of the drum (Schlett and Lungu, 1999). They are caused by Faraday’s induction law and are developing as a reaction to the fluctuations of the field observed by the particle. The complex interactions between the magnetic field and the induced eddy currents lead to the appearance of electrodynamic actions upon conductive nonferrous particles and are responsible for the separation process. When a particle moves through the magnetic field, it experiences changes of size and orientation of the field due to its own translational and rotational motion as well as due to the rotation of the drum. For magnet drums such as the ADECS, with k poles and spinning with angular velocity x, the field outside the surface r = Rd of the drum can be approximated by its fundamental mode (i.e., its first Fourier component) (Rem, 1999): kþ1 Br R cosk ð/ xt Þ B¼ : ð1Þ ib d sink ð/ xt Þ B/ r If the particle is sufficiently small with respect to the pole width k of the drum, where 2pRd = kk, the variations of the drum field within the particle are smooth and the eddy-current distribution can be treated as a magnetic dipole. In this case, both the force F and the torque T can be expressed in terms of the field gradient and the magnetic moment M of the particle (Rem et al., 1996): F ¼ ðMjÞB ¼ Mx jBx þ My jBy þ Mz jBz
ð2Þ
T ¼ M B;
ð3Þ
where: 1 M¼ 2
Z
r jdV
v
with j the current density of the eddy current in the particle. If the global behavior of the particle’s magnetic moment is known, the force and torque upon a conductive nonferrous particle can be estimated by standard magnetic theory. Because these expressions have similar terms, there can be written relations between the two components of the electrodynamic force and the torque. So, the component of the force tangential to the magnet surface, F t, and the component away from the surface (i.e. the radial component), F r, are (Rem, 1999): 2pd T Ft ¼ k d Fr ¼ sm0 ðx XÞrd 2 Ft ;
ð4Þ
with d the characteristic size of the particle, k the width of a pair of poles, s a shape factor, x the angular velocity of the magnetic field, X the angular velocity of the particle, r the electric conductivity of the particle, and l 0 the magnetic permeability of vacuum. The torque T makes the particle spins in opposite direction as the magnetic field, which rotates counterclockwise, if the field is generated by a clockwise rotation of the eddy-current rotor (if the rotation of the rotor is forward, the nonferrous particle will roll backward). The expression of the torque is finally given by: T ¼ cjBj2 V ðx XÞrd 2
ð5Þ
where B is the magnetic induction at the position of the particle, V is the volume of the particle and c is a factor depending on the shape and orientation of the particle, which is documented in Table 1 (Rem, 1999). For small to medium-sized particles the force T / R, which can potentially be derived from the eddy-current torque, is larger than the tangential force that is conventionally used for the separation on a conventional rotary drum separator (i.e. the HDECS). Such a separator, the conversion of the torque to a linear force through friction with a solid surface (i.e. the conveyor
M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30 Table 1 Parameters of expressions 4, 5 and 11 for particles of several shapes and parallel (||) or perpendicular (?) orientations of their axis of symmetry with respect to the rotation axis of the magnet drum Shape
c
d
c
sphere cylinder || cylinder ? disk || disk ?
1/40 1/16 3/64 1/12 1/64
D D D d D
1/4 1/2 9D 2 / 16L 2 2d 2 / 3D 2 1/4
25
In this case the sliding motion of the particle will produce a friction force: Ff ¼ fd mg
ð8Þ
where f d is the coefficient of dynamic friction. The tangential and the frictional forces are always in opposite directions, as shown in Fig. 2, and a transition of the direction of motion on a horizontal plane takes place when:
D stands for particle diameter, L for length and d for thickness.
Ft ¼ fd mg
belt) is generally not efficient because it is limited by the friction factor, which besides being small, is also subject to random effects. The tangential force, which is always counteracting the friction, may be in case of small particles, of the same order of magnitude as the frictional force. In this case the expressions (4) for the force show that a substantial spin of the particle will reduce the eddy-current forces. This means that for small particles, in case of conventional rotary drum separators, the spinning the spinning motion may limit the separation force. A solution to the small particles problem is to convert the eddy-current torque into a useful separation force, as the concept of the angular rotary drum separator, which will be presented below. All the actions upon a nonferrous particle lying on the support (the conveyor belt) of the separation device (the ADECS) above the rotating magnets are shown in Fig. 2; Fsup is the support force. When the particles get near the active zone of the field, both the force and the torque increase up to the point for which the particles are lifted from the support surface. For the smallest particles (particles of size under 5 mm), only the tangential force and the torque, in competition with the frictional force, are relevant for the separation. As shown in Fig. 2a particle will start to roll over the support and becomes to rotate as soon as:
The strongly conducting particles will jump if the torque is sufficiently strong. This is the so called jump effect, which is responsible for the separation of the particles in the case of the ADECS. In case of HDECS this effect is a disadvantage: the T / R factor makes the small particles jump up to early and fall close over the rotor into the reject, which lead to a decrease of the product purity. In case of the ADECS this disadvantage was avoided, due to the angular positioning of the drum. Below, a simple criterion for deciding whether a particle of a given shape and material is able to jump to a certain height h above the surface by the action of the magnetic field will be derived. For a spinning particle, part of its rotational motion is converted during the flight to a velocity m, inclined with an angle b versus the surface of the belt (as in Figs. 2 and 3), function of n — revolution of the rotor and u — the velocity displacement of the belt. The magnetic torque T restores the loss of rotational energy of the particle during its passage into the high intensity rotating field near the rotor. For high values of m, the residence time of the particle in the
T cmg: d
ð9Þ
ð6Þ
In these conditions the small particles rotate on the belt. If f s is the coefficient of static friction, the condition for sliding rotation is: T Nfs mg: d
ð7Þ
Fig. 2. Forces acting on a nonferrous particle lying on the belt, above the rotating magnets.
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M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30
Fig. 3. Overview of the ADECS.
strong field near the surface is relatively small, leading to a small increase of the particle spin during the field and a smaller value of v after the impact with the surface. The actual value of v and the corresponding jump height h = (m 2 / 2g)sin2 b is therefore a balance of the loss and gain of rotational motion during the flight and impact of the particle, respectively. The particle will hit the surface at a typical distance r = (m 2 / g)sin2b away from its center of mass as projected to the plane of the surface, as in Fig. 3. If the collision has low elasticity (as it usually has), the momentum balance shows that in order to reach a certain value m, the magnetic torque should increase the angular velocity of the particle from an initial value X i = m / r to a final value X f = (m / r)(1 + 2mr 2 / I) during the flight, with m and I being the mass and moment of inertia. Since Eq. (5) for the magnetic torque shows that the angular velocity X of the particles can never exceed the angular velocity x of the field, the rotation speed of the rotor should be at least sufficient to make x z X f in order for some of the particles to jump to a height h. Suppose now, that we have two kinds of particles, of different materials or shapes. The increase of the angular velocity during their flight follows by integrating the magnetic torque during the passage of the particle out of and into the magnetic field of the rotor (Rem, 1999): jBj ¼ be2pz=k
ð10Þ
where b is the magnetic induction at the surface and z is the position of the particle above the surface. If we neglect, for ease of analysis, the initial particle rotation and the variation of v in the magnetic field zone, the final value for the angular velocity of the particles is: ð11Þ Xf ¼ x 1 ecAm Ad with three different factors c, A m and A d , depending on the shape of the particle, its density q and conductivity r, and the design of the separator, respectively: cmd 2 I
ð12Þ
Am ¼
r q
ð13Þ
Ad ¼
b2 k 2pm
ð14Þ
c¼
For typical values of the design parameters (b = 0.35 T, k = 0.06 m, h = 0.02 m) we get A d c 0.002. Table 1 shows that the shape factor c is typically 0.25 and Table 2 gives values of r / q, Table 2 Density, conductivity and separation factor for several materials Material
q [kg/m3]
r [1/m V]
r /q
Aluminum Copper Lead
2700 8900 11400
27 106 56 106 5 106
10000 6300 440
M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30
27
3. Engineering and operation
Fig. 4. The trajectories of the particles in the separator.
named the separation factor, for several metals. From these values, it follows that the product of the three different factors is about 0.2 for flat or granular lead particles, whereas it is about 5 for aluminum particles of the same shape. Copper wires give values of between 0.5 and 2, depending on their diameter to length ratio. Clearly, it is possible to make one type of particle jump to the maximum height h while another type of particle does not reach the required angular velocity, by varying the rotor speed and one of the design parameters. (i.e. the incident angle a).
The principle outline of ADECS is presented in Fig. 2. The drum (1), the revolution of which can be varied from 0 to 4500 r/min is made of soft magnetic steel and covered with rows of permanent magnets (2). The magnets are alternately oriented N–S and S–N and the drum is placed oblique with an angle a under the surface of the conveyor belt (3), as in Fig. 2. The angle b is made by the jumped particles velocity m versus the surface of the conveyor belt. The feed material is introduced into the active zone of the field by the conveyor belt over the spinning angular drum. Only half of the conveyor belt, on its front part, is used to feed the material. Consequently, the length of the magnets are just about half of the belt width. The material is placed over the conveyor belt that is moving at a velocity u, which is a function of physical properties of the particles. The other half of the belt is used to collect the jumped particles, after they fall back to the belt. The dielectric particles, on which no electrodynamics forces are acting, or the poorly conducting particles, on which the electrodynamic actions are too weak to move them, remain on the surface of the conveyor belt. They are moving on the same trajectory
Fig. 5. G versus R for Cu, function of the angle a´ and revolution n of the drum: n 1 = 3000 r/min, n 2 = 3500 r/min, n 3 = 4000 r/min, n 4 = 4500 r/min.
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M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30
Fig. 6. G versus R for Pb, function of the angle a and revolution n of the drum: n 1 = 3000 r/min, n 2 = 3500 r/min, n 3 = 4000 r/min, n 4 = 4500 r/min.
than the initial and fall from the back part of the belt in the compartment I of the collector box (4). The strongly conducting particle, upon which electrodynamic force becomes significant at a certain value of drum revolution n, start to execute, under the action of torque T, jumps when it reaches the active zone of the field. Due to the incident angle a between the axis of the rotor and the direction dis-
placement of the feed material (the same with the direction displacement of the belt), after the jump they fall on the belt at distance r away from their center of mass on the other half of the belt as shown in Fig. 4, and obtains a trajectory parallel to that of poorly conducting particles. Finally, they fall from the back part of the belt in compartment II of the collecting box (4) leading to separation.
Fig. 7. G versus R for Cu, function of the angle a and revolution n of the drum: n 1 = 1000 r/min, n 2 = 1200 r/min, n 3 = 1400 r/min, n 4 = 1600 r/min.
M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30
The incident angle a, the disc revolution n and the velocity u of the belt are the quantities which determine the height of the particles jumps and consequently the separation quality. Therefore, these parameters must be properly adjusted for each material.
4. Experimental results Experimentally, the quantities grade G (ratio of the mass of a material in the product and the product as a whole) and recovery R (ratio of the mass of a material in the product and the mass of that same material in the feed) has been determined for two types of electro technical wastes, namely: 4.1. Mixture A Electrical cables Cu and Pb mixture containing particles of irregular shapes and dimensions between 2.5–4 mm. The proportions are 64% Cu to 36% Pb. Fig. 5 shows the grade–recovery diagram for Cu collected in compartment II and Fig. 6 for Pb collected in compartment I, respectively. G was plotted versus R depending on the incident angle a at different values of the drum revolution n. The velocity displacement u of the belt was fixed at 0.5 m/s.
29
4.2. Mixture B Cu and Al mixture containing particles of irregular shapes and dimensions between 2–5 mm. The proportions are 40% Cu to 60% Al. Fig. 7 shows the grade– recovery diagram for Cu collected in compartment I and Fig. 8 for Al collected in compartment II, respectively. G was plotted versus R depending on the incident angle a at different values of the drum revolution n. The velocity displacement u of the belt was fixed at 0.5 m/s.
5. Discussion The separation experiments on the Cu–Pb mixture shows that with increasing rotor speed, an increasing amount of copper particles are able to jump to the level of the upper product (the material collected in compartment II after jump), while the lead particles remain largely on the surface of the belt. At an angle, a of 458 and a rotation speed of 3500 rpm, the lead particles start to contaminate the upper product, while the recovery of copper in the upper product is at a maximum at a somewhat higher speed of 4500 rpm. It is clear that at still higher speeds, the lead particles reach a maximum grade as well. A similar behavior is
Fig. 8. G versus R for Al, function of the angle a and revolution n of the drum: n 1 = 1000 r/min, n 2 = 1200 r/min, n 3 = 1400 r/min, n 4 = 1600 r/min.
30
M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30
apparent from the data for the aluminum–copper mixture, with aluminum reaching the upper product level first. A 100% grade means that the product contains only the useful material (i.e. copper in compartment II in case of Mixture A, and a 100% recovery means that all of that material ends up in the product. So, a compromise must to be struck between the purity of the product, which will set the price/ton, and the amount of the product. The data show that the order in which the materials reach the upper product level was well predicted by theory. Using the grade–recovery diagram of a separation process, to select the economic optimum, the experimental results show that for a given value of the incident angle a, the maximum separation grade is obtained at an intermediate value of the drum revolution (i.e. at n = 3500–4000 r/min for Cu in case of Mixture A. At high values of the drum revolution, which imply high values of the electrodynamic force F t and torque T, the strongly conducting particles are strongly repelled. They can hit the poorly conducting particles and modify their trajectory on the belt. Thus, a fraction of the strongly conducting as well as poorly conducting particles falls into another compartment and contaminate the product. This effect turned out to be useful, because for increasing the efficiency of the separation process one does not need high values of the drum revolution, which in fact can be very dangerous, but a good arrangement of the system geometry. An angular position for the rotor makes the jumped particles to achieve another trajectory, avoiding collisions and the mixture with other particles. As can be observed, the maximum separation efficiency was obtained in all cases at an incident angle a = 458.
6. Conclusions The ADECS successfully separates wastes containing conductive non-ferrous and non-conductive particles or strongly conducting and poorly conducting nonferrous particles, respectively. Besides its high efficiency is close to the one of the usual dynamic eddy-current separators (i.e. the HDECS), the ADECS has the advantage of a low cost due to the reduced length of the permanent magnets and the placement of the drum under the belt (not within the pulley), fact that implies absence of supplementary machinery. Another advantage of this solution is that the feed can be brought closer to the rotor, so that less of the high field region in lost. A disadvantage is that a reduction of the field region can seem to relate a reduced throughput, but this can be counteracting through an increase the speed of the belt.
References Rem, P.C., Leest, P.A., van den Akker, A.J., 1996. A model for eddy-current separation. International Journal of Mineral Processing 49, 193. Rem, P.C., 1999. Eddy Current Separation. Eburon Delft, the Netherlands. Schlett, Z., Lungu, M., 1999. Vertical Eddy-currents Separator for Electronic Wastes. Proc. 50. Bergund Ha¨nnischer Tag, vol. 2. Technische Universita¨t Bergakademie Freiberg, Germany, Forschungshefte Kolloquium, pp. 395 – 400. Schloemann, E., 1975. Separation of nonmagnetic metals from solid waste by permanent magnets. Journal of Applied Physics 46 (11), 5012. Van der Valk, H.J.L., Braam, B.C., Dalmijn, W.L., 1986. Eddycurrent separation by permanent magnets: Part I. Theory. Resources and Conservation 12, 233.
Separation of small nonferrous particles using an angular rotary drum eddy-current separator with permanent magnets Mihai Lungu * Department of Physics, West University Timisoara, Blv. V. Parvan No. 4, Timisoara 1900, Romania Received 30 December 2004; received in revised form 16 July 2005; accepted 18 July 2005 Available online 24 August 2005
Abstract The paper presents a method for separating the small metallic nonferrous particles from two component nonferrous mixtures using a new type of dynamic eddy-current separator with permanent magnets. The so called Angular Drum Eddy-Current Separator (ADECS) consists of a horizontal rotary drum covered with permanent magnets, alternately N–S and S–N oriented. The rotor is placed oblique, under the superior part of a horizontal conveyor belt, coplanar with its surface. The axis of the drum and the direction of displacement of the belt make a certain angle, depending on the physical properties of the particles subjected to the separation process. The separator functions on the basis of the jump effect of the strongly conducting particles which assume different trajectories in the active zone of the field, namely, upper part of the drum. The experimental results and comments regarding the values obtained for grade and recovery for wastes consisting in Cu–Pb and Cu–Al mixtures are given. D 2005 Elsevier B.V. All rights reserved. Keywords: Eddy-current separator; Grade; Nonferrous; Poorly conducting particles; Strongly conducting particles; Recovery
1. Introduction Eddy-current separation methods are used both for recovery and purification of conductive nonferrous metals (Cu, Al, Pb) and also for separating various nonferrous metals from each other (Rem, 1999; Schloemann, 1975). In eddy-current separators, the eddy currents are induced in the nonferrous metallic particles due to the
* Tel.: +40 256494068; fax: +40 256490333. E-mail address: [email protected]. 0301-7516/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.minpro.2005.07.003
changing magnetic field in the active zone of the separator. The interaction between these currents and the magnetic field results into repulsive electrodynamic forces on the metallic particles and so into their separation from nonconductive ones, or from each other (Rem et al., 1996; Schlett and Lungu, 1999). The time dependent change of the magnetic field can be obtained by different devices. Eddy-current dynamic separators with permanent magnets represent a class of separators substantially improved in the last few years, where the magnetic field is generated by machinery with moving permanent magnets. By using permanent magnets, strong fields can be generated,
M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30
therefore the operation costs of eddy-current separation are considerably reduced and the construction of the equipment can be less complex. The eddy-current separators have been developed for the recovery of nonferrous metals from mixtures of waste materials, i.e. shredded car scrap, granulated power cables and municipal solid wastes (Schloemann, 1975; Van der Valk et al., 1986). Although eddy-current separation is used for a wide range of particles sizes and materials, different rotor designs are actually used, the specific choice depending on the feed characteristics and the separation. Machines designed for small particles have many magnet poles of small width, while machines for large particles have a few large poles. These machineries have the same problem, namely a high cost because of the length of the permanent magnets. Yet, the main problems associated with eddy-current separation are those referring to the selective separation of conductive nonferrous particles smaller than 5 mm from nonconductive ones or one from each other, while reducing the cost of the separation process. These particles are difficult to recover with conventional eddy-current separators of the rotary drum type, and are even harder to separate these fractions into the various alloys. The reason is that, for such particles eddy-current separation force (i.e. the tangential force which will be described in the theoretical part) produces acceleration less than the acceleration gravity. As a consequence, the frictional forces which appear due to movement of the particles and acting in the direction opposite to the tangential force will tend to dominate. This paper describes a new type of eddy-current separator with permanent magnets, namely, the angular-drum eddy-current separator (ADECS), designed for separation with a higher efficiency the mixtures of conductive nonferrous and nonconductive particles, or strongly conducting and poorly conducting nonferrous particles, smaller than 5 mm. The separator consists of a horizontal spinning drum, covered with rows of permanent magnets, alternately N–S and S–N oriented, placed oblique under the superior part of a horizontal conveyor belt, coplanar with its surface, as in Fig. 1. The axis of the drum makes an angle a with the direction of the belt. This angle depends on the physical properties of the particles subjected to the separation process, i.e., the elec-
23
Fig. 1. A basic diagram of the separator.
tric conductivity, shape, dimensions and their proportions in the waste. A similar separator is the horizontal drum eddycurrent separator (HDECS) which uses a conveyor belt to feed the material over a rotor with permanent magnets, mounted concentrically within the pulley of the belt. The length of the magnets is equal with the active width of the belt, and the feeding of the particles is made on the whole breadth of the belt. Unlike HDECS, in the case of the ADECS the feeding of the particles (from constructive reasons) is made only on the half of the belt width and, consequently, the magnets are long just about half than the belt width. So, the first reason to use an angular drum is the lower cost of the separation equipment than the conventional HDECS. The feed material is introduced into the active zone of the field by the conveyor belt over the rotary angular drum, and the functioning of the separator is based on the jump effect of the strongly conducting particles. This effect, responsible for the separation of the particles in the case of ADECS and undesired in the functioning of the conventional HDECS, will be described in the theoretical part of the present paper. Under the combined actions of electromagnetic interactions, gravitational and frictional forces, the particles of the feed material describe various trajectories on the surface of the belt, depending on their physical properties. Thus, the poorly conducting and strongly conducting particles or conductive nonferrous and nonconductive particles obtain different trajectories and leave the end part of the belt on different ways, leading finally to their separation. The drum and the belt are coplanar and made the angle a in the horizontal plane that is the incident
24
M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30
angle for the feeding particles, in order to obtain a maximum efficiency of the separation process. The repelled particles are represented by the strongly conducting particles in the case of mixtures containing strongly conducting–poorly conducting particles and conductive non-ferrous particles in the case of mixtures containing conductive non-ferrous–nonconductive particles, respectively.
2. Theoretical considerations Eddy currents are induced in a conductive nonferrous particle placed in the active zone of the separator as a response to the magnetic field, which changes rapidly in time due to the rotation of the drum (Schlett and Lungu, 1999). They are caused by Faraday’s induction law and are developing as a reaction to the fluctuations of the field observed by the particle. The complex interactions between the magnetic field and the induced eddy currents lead to the appearance of electrodynamic actions upon conductive nonferrous particles and are responsible for the separation process. When a particle moves through the magnetic field, it experiences changes of size and orientation of the field due to its own translational and rotational motion as well as due to the rotation of the drum. For magnet drums such as the ADECS, with k poles and spinning with angular velocity x, the field outside the surface r = Rd of the drum can be approximated by its fundamental mode (i.e., its first Fourier component) (Rem, 1999): kþ1 Br R cosk ð/ xt Þ B¼ : ð1Þ ib d sink ð/ xt Þ B/ r If the particle is sufficiently small with respect to the pole width k of the drum, where 2pRd = kk, the variations of the drum field within the particle are smooth and the eddy-current distribution can be treated as a magnetic dipole. In this case, both the force F and the torque T can be expressed in terms of the field gradient and the magnetic moment M of the particle (Rem et al., 1996): F ¼ ðMjÞB ¼ Mx jBx þ My jBy þ Mz jBz
ð2Þ
T ¼ M B;
ð3Þ
where: 1 M¼ 2
Z
r jdV
v
with j the current density of the eddy current in the particle. If the global behavior of the particle’s magnetic moment is known, the force and torque upon a conductive nonferrous particle can be estimated by standard magnetic theory. Because these expressions have similar terms, there can be written relations between the two components of the electrodynamic force and the torque. So, the component of the force tangential to the magnet surface, F t, and the component away from the surface (i.e. the radial component), F r, are (Rem, 1999): 2pd T Ft ¼ k d Fr ¼ sm0 ðx XÞrd 2 Ft ;
ð4Þ
with d the characteristic size of the particle, k the width of a pair of poles, s a shape factor, x the angular velocity of the magnetic field, X the angular velocity of the particle, r the electric conductivity of the particle, and l 0 the magnetic permeability of vacuum. The torque T makes the particle spins in opposite direction as the magnetic field, which rotates counterclockwise, if the field is generated by a clockwise rotation of the eddy-current rotor (if the rotation of the rotor is forward, the nonferrous particle will roll backward). The expression of the torque is finally given by: T ¼ cjBj2 V ðx XÞrd 2
ð5Þ
where B is the magnetic induction at the position of the particle, V is the volume of the particle and c is a factor depending on the shape and orientation of the particle, which is documented in Table 1 (Rem, 1999). For small to medium-sized particles the force T / R, which can potentially be derived from the eddy-current torque, is larger than the tangential force that is conventionally used for the separation on a conventional rotary drum separator (i.e. the HDECS). Such a separator, the conversion of the torque to a linear force through friction with a solid surface (i.e. the conveyor
M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30 Table 1 Parameters of expressions 4, 5 and 11 for particles of several shapes and parallel (||) or perpendicular (?) orientations of their axis of symmetry with respect to the rotation axis of the magnet drum Shape
c
d
c
sphere cylinder || cylinder ? disk || disk ?
1/40 1/16 3/64 1/12 1/64
D D D d D
1/4 1/2 9D 2 / 16L 2 2d 2 / 3D 2 1/4
25
In this case the sliding motion of the particle will produce a friction force: Ff ¼ fd mg
ð8Þ
where f d is the coefficient of dynamic friction. The tangential and the frictional forces are always in opposite directions, as shown in Fig. 2, and a transition of the direction of motion on a horizontal plane takes place when:
D stands for particle diameter, L for length and d for thickness.
Ft ¼ fd mg
belt) is generally not efficient because it is limited by the friction factor, which besides being small, is also subject to random effects. The tangential force, which is always counteracting the friction, may be in case of small particles, of the same order of magnitude as the frictional force. In this case the expressions (4) for the force show that a substantial spin of the particle will reduce the eddy-current forces. This means that for small particles, in case of conventional rotary drum separators, the spinning the spinning motion may limit the separation force. A solution to the small particles problem is to convert the eddy-current torque into a useful separation force, as the concept of the angular rotary drum separator, which will be presented below. All the actions upon a nonferrous particle lying on the support (the conveyor belt) of the separation device (the ADECS) above the rotating magnets are shown in Fig. 2; Fsup is the support force. When the particles get near the active zone of the field, both the force and the torque increase up to the point for which the particles are lifted from the support surface. For the smallest particles (particles of size under 5 mm), only the tangential force and the torque, in competition with the frictional force, are relevant for the separation. As shown in Fig. 2a particle will start to roll over the support and becomes to rotate as soon as:
The strongly conducting particles will jump if the torque is sufficiently strong. This is the so called jump effect, which is responsible for the separation of the particles in the case of the ADECS. In case of HDECS this effect is a disadvantage: the T / R factor makes the small particles jump up to early and fall close over the rotor into the reject, which lead to a decrease of the product purity. In case of the ADECS this disadvantage was avoided, due to the angular positioning of the drum. Below, a simple criterion for deciding whether a particle of a given shape and material is able to jump to a certain height h above the surface by the action of the magnetic field will be derived. For a spinning particle, part of its rotational motion is converted during the flight to a velocity m, inclined with an angle b versus the surface of the belt (as in Figs. 2 and 3), function of n — revolution of the rotor and u — the velocity displacement of the belt. The magnetic torque T restores the loss of rotational energy of the particle during its passage into the high intensity rotating field near the rotor. For high values of m, the residence time of the particle in the
T cmg: d
ð9Þ
ð6Þ
In these conditions the small particles rotate on the belt. If f s is the coefficient of static friction, the condition for sliding rotation is: T Nfs mg: d
ð7Þ
Fig. 2. Forces acting on a nonferrous particle lying on the belt, above the rotating magnets.
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M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30
Fig. 3. Overview of the ADECS.
strong field near the surface is relatively small, leading to a small increase of the particle spin during the field and a smaller value of v after the impact with the surface. The actual value of v and the corresponding jump height h = (m 2 / 2g)sin2 b is therefore a balance of the loss and gain of rotational motion during the flight and impact of the particle, respectively. The particle will hit the surface at a typical distance r = (m 2 / g)sin2b away from its center of mass as projected to the plane of the surface, as in Fig. 3. If the collision has low elasticity (as it usually has), the momentum balance shows that in order to reach a certain value m, the magnetic torque should increase the angular velocity of the particle from an initial value X i = m / r to a final value X f = (m / r)(1 + 2mr 2 / I) during the flight, with m and I being the mass and moment of inertia. Since Eq. (5) for the magnetic torque shows that the angular velocity X of the particles can never exceed the angular velocity x of the field, the rotation speed of the rotor should be at least sufficient to make x z X f in order for some of the particles to jump to a height h. Suppose now, that we have two kinds of particles, of different materials or shapes. The increase of the angular velocity during their flight follows by integrating the magnetic torque during the passage of the particle out of and into the magnetic field of the rotor (Rem, 1999): jBj ¼ be2pz=k
ð10Þ
where b is the magnetic induction at the surface and z is the position of the particle above the surface. If we neglect, for ease of analysis, the initial particle rotation and the variation of v in the magnetic field zone, the final value for the angular velocity of the particles is: ð11Þ Xf ¼ x 1 ecAm Ad with three different factors c, A m and A d , depending on the shape of the particle, its density q and conductivity r, and the design of the separator, respectively: cmd 2 I
ð12Þ
Am ¼
r q
ð13Þ
Ad ¼
b2 k 2pm
ð14Þ
c¼
For typical values of the design parameters (b = 0.35 T, k = 0.06 m, h = 0.02 m) we get A d c 0.002. Table 1 shows that the shape factor c is typically 0.25 and Table 2 gives values of r / q, Table 2 Density, conductivity and separation factor for several materials Material
q [kg/m3]
r [1/m V]
r /q
Aluminum Copper Lead
2700 8900 11400
27 106 56 106 5 106
10000 6300 440
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3. Engineering and operation
Fig. 4. The trajectories of the particles in the separator.
named the separation factor, for several metals. From these values, it follows that the product of the three different factors is about 0.2 for flat or granular lead particles, whereas it is about 5 for aluminum particles of the same shape. Copper wires give values of between 0.5 and 2, depending on their diameter to length ratio. Clearly, it is possible to make one type of particle jump to the maximum height h while another type of particle does not reach the required angular velocity, by varying the rotor speed and one of the design parameters. (i.e. the incident angle a).
The principle outline of ADECS is presented in Fig. 2. The drum (1), the revolution of which can be varied from 0 to 4500 r/min is made of soft magnetic steel and covered with rows of permanent magnets (2). The magnets are alternately oriented N–S and S–N and the drum is placed oblique with an angle a under the surface of the conveyor belt (3), as in Fig. 2. The angle b is made by the jumped particles velocity m versus the surface of the conveyor belt. The feed material is introduced into the active zone of the field by the conveyor belt over the spinning angular drum. Only half of the conveyor belt, on its front part, is used to feed the material. Consequently, the length of the magnets are just about half of the belt width. The material is placed over the conveyor belt that is moving at a velocity u, which is a function of physical properties of the particles. The other half of the belt is used to collect the jumped particles, after they fall back to the belt. The dielectric particles, on which no electrodynamics forces are acting, or the poorly conducting particles, on which the electrodynamic actions are too weak to move them, remain on the surface of the conveyor belt. They are moving on the same trajectory
Fig. 5. G versus R for Cu, function of the angle a´ and revolution n of the drum: n 1 = 3000 r/min, n 2 = 3500 r/min, n 3 = 4000 r/min, n 4 = 4500 r/min.
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M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30
Fig. 6. G versus R for Pb, function of the angle a and revolution n of the drum: n 1 = 3000 r/min, n 2 = 3500 r/min, n 3 = 4000 r/min, n 4 = 4500 r/min.
than the initial and fall from the back part of the belt in the compartment I of the collector box (4). The strongly conducting particle, upon which electrodynamic force becomes significant at a certain value of drum revolution n, start to execute, under the action of torque T, jumps when it reaches the active zone of the field. Due to the incident angle a between the axis of the rotor and the direction dis-
placement of the feed material (the same with the direction displacement of the belt), after the jump they fall on the belt at distance r away from their center of mass on the other half of the belt as shown in Fig. 4, and obtains a trajectory parallel to that of poorly conducting particles. Finally, they fall from the back part of the belt in compartment II of the collecting box (4) leading to separation.
Fig. 7. G versus R for Cu, function of the angle a and revolution n of the drum: n 1 = 1000 r/min, n 2 = 1200 r/min, n 3 = 1400 r/min, n 4 = 1600 r/min.
M. Lungu / Int. J. Miner. Process. 78 (2005) 22–30
The incident angle a, the disc revolution n and the velocity u of the belt are the quantities which determine the height of the particles jumps and consequently the separation quality. Therefore, these parameters must be properly adjusted for each material.
4. Experimental results Experimentally, the quantities grade G (ratio of the mass of a material in the product and the product as a whole) and recovery R (ratio of the mass of a material in the product and the mass of that same material in the feed) has been determined for two types of electro technical wastes, namely: 4.1. Mixture A Electrical cables Cu and Pb mixture containing particles of irregular shapes and dimensions between 2.5–4 mm. The proportions are 64% Cu to 36% Pb. Fig. 5 shows the grade–recovery diagram for Cu collected in compartment II and Fig. 6 for Pb collected in compartment I, respectively. G was plotted versus R depending on the incident angle a at different values of the drum revolution n. The velocity displacement u of the belt was fixed at 0.5 m/s.
29
4.2. Mixture B Cu and Al mixture containing particles of irregular shapes and dimensions between 2–5 mm. The proportions are 40% Cu to 60% Al. Fig. 7 shows the grade– recovery diagram for Cu collected in compartment I and Fig. 8 for Al collected in compartment II, respectively. G was plotted versus R depending on the incident angle a at different values of the drum revolution n. The velocity displacement u of the belt was fixed at 0.5 m/s.
5. Discussion The separation experiments on the Cu–Pb mixture shows that with increasing rotor speed, an increasing amount of copper particles are able to jump to the level of the upper product (the material collected in compartment II after jump), while the lead particles remain largely on the surface of the belt. At an angle, a of 458 and a rotation speed of 3500 rpm, the lead particles start to contaminate the upper product, while the recovery of copper in the upper product is at a maximum at a somewhat higher speed of 4500 rpm. It is clear that at still higher speeds, the lead particles reach a maximum grade as well. A similar behavior is
Fig. 8. G versus R for Al, function of the angle a and revolution n of the drum: n 1 = 1000 r/min, n 2 = 1200 r/min, n 3 = 1400 r/min, n 4 = 1600 r/min.
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apparent from the data for the aluminum–copper mixture, with aluminum reaching the upper product level first. A 100% grade means that the product contains only the useful material (i.e. copper in compartment II in case of Mixture A, and a 100% recovery means that all of that material ends up in the product. So, a compromise must to be struck between the purity of the product, which will set the price/ton, and the amount of the product. The data show that the order in which the materials reach the upper product level was well predicted by theory. Using the grade–recovery diagram of a separation process, to select the economic optimum, the experimental results show that for a given value of the incident angle a, the maximum separation grade is obtained at an intermediate value of the drum revolution (i.e. at n = 3500–4000 r/min for Cu in case of Mixture A. At high values of the drum revolution, which imply high values of the electrodynamic force F t and torque T, the strongly conducting particles are strongly repelled. They can hit the poorly conducting particles and modify their trajectory on the belt. Thus, a fraction of the strongly conducting as well as poorly conducting particles falls into another compartment and contaminate the product. This effect turned out to be useful, because for increasing the efficiency of the separation process one does not need high values of the drum revolution, which in fact can be very dangerous, but a good arrangement of the system geometry. An angular position for the rotor makes the jumped particles to achieve another trajectory, avoiding collisions and the mixture with other particles. As can be observed, the maximum separation efficiency was obtained in all cases at an incident angle a = 458.
6. Conclusions The ADECS successfully separates wastes containing conductive non-ferrous and non-conductive particles or strongly conducting and poorly conducting nonferrous particles, respectively. Besides its high efficiency is close to the one of the usual dynamic eddy-current separators (i.e. the HDECS), the ADECS has the advantage of a low cost due to the reduced length of the permanent magnets and the placement of the drum under the belt (not within the pulley), fact that implies absence of supplementary machinery. Another advantage of this solution is that the feed can be brought closer to the rotor, so that less of the high field region in lost. A disadvantage is that a reduction of the field region can seem to relate a reduced throughput, but this can be counteracting through an increase the speed of the belt.
References Rem, P.C., Leest, P.A., van den Akker, A.J., 1996. A model for eddy-current separation. International Journal of Mineral Processing 49, 193. Rem, P.C., 1999. Eddy Current Separation. Eburon Delft, the Netherlands. Schlett, Z., Lungu, M., 1999. Vertical Eddy-currents Separator for Electronic Wastes. Proc. 50. Bergund Ha¨nnischer Tag, vol. 2. Technische Universita¨t Bergakademie Freiberg, Germany, Forschungshefte Kolloquium, pp. 395 – 400. Schloemann, E., 1975. Separation of nonmagnetic metals from solid waste by permanent magnets. Journal of Applied Physics 46 (11), 5012. Van der Valk, H.J.L., Braam, B.C., Dalmijn, W.L., 1986. Eddycurrent separation by permanent magnets: Part I. Theory. Resources and Conservation 12, 233.